month - a unit of time, used with calendars, that is approximately as long as a natural orbital period of the Moon

$1,100 per month for 10 years, if the account earns 2% per year

$1,100 per month for 10 years, if the account earns 2% per year
What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?
Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly.
1100 per month. * 12 months in a year = 13,200 per year in deposit
Since we matched interest crediting period with deposits, we now want to know:
If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years?
This is an annuity, which is a constant stream of payments with interest crediting at a certain period.
[SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B]
[B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE]
[B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02
[B]AV =[/B]13200 * (1.02^10 - 1)/0.02
[B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02
[B]AV =[/B]13200 * 0.21899441999476/0.02
[B]AV = [/B]2890.7263439308/0.02
[B]AV = 144,536.32[/B]

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m months.
Set up the cost function C(m) where m is the number of months you rent:
C(m) = Monthly membership fee * m + initial fee
[B]C(m) = 30m + 100[/B]

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How much money will be in the account after 7 years?
7 years * 12 months per year = 84 periods.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=100&nval=84&int=3&pl=Monthly']compound interest calculator[/URL], we get an account balance of:
[B]123.34[/B]

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, w

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years
So we have:
[LIST]
[*]$300 principal
[*]13 * 2 = 26 periods for n
[*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period
[/LIST]
Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get:
[B]$831.74[/B]

$4700 at 3.5% for 6 years compounded monthly

$4700 at 3.5% for 6 years compounded monthly
6 years = 12*6 = 72 months or compounding periods.
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=4700&nval=72&int=3.5&pl=Monthly']balance with interest calculator[/URL], we get a final balance of:
[B]$5,796.51[/B]

4K a month how much in a year

4K a month how much in a year
4K = 4000, so we have:
4000 per month * 12 months / year = [B]48,000 per year[/B]

72 pounds and increases by 3.9 pounds per month

72 pounds and increases by 3.9 pounds per month
Let m be the number of months. We write the algebraic expression below:
[B]3.9m + 72[/B]

A $1,000 deposit is made at a bank that pays 12% compounded monthly. How much will you have in your

A $1,000 deposit is made at a bank that pays 12% compounded monthly. How much will you have in your account at the end of 10 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=10000&nval=120&int=12&pl=Monthly']compound interest calculator[/URL] with time = 10 years * 12 months per year = 120, we get:
[B]33,003.87[/B]

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200?
We want to know x for the equation:
654000 - 1800x = 409200
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]136 months[/B]

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x repre

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation
y = 675 - 18x
The y-intercept is found when x is 0:
y = 675 - 18(0)
y = 675 - 0
y = 675
The x-intercept is found when y is 0:
0 = 675 - 18x
[URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get:
x = 37.5

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. I

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?
Let m be the number of months. Our balance is denoted by B(m):
B(m) = 85 - 7.5m
The question asks when B(m) is less than 0. So we set up an inequality:
85 - 7.5m < 0
To solve this inequality for m, [URL='https://www.mathcelebrity.com/1unk.php?num=85-7.5m%3C0&pl=Solve']we type it in our search engine[/URL] and we get:
m > 11.3333
We round up to the next whole integer and get [B]m = 12[/B]

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The ave

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
Profit = Revenue - Cost
Let the number of bikes be b.
Revenue = 80b
Cost = 60b + 1500
Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other:
60b + 1500 = 80b
We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]75[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Let the number of bikes be b.
Set up our cost function, where it costs $45 per bike to produce
C(b) = 45b
Set up our revenue function, where we earn $95 per sale for each bike:
R(b) = 95b
Set up our profit function, which is how much we keep after a sale:
P(b) = R(b) - C(b)
P(b) = 95b - 45b
P(b) = 50b
The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750
50b = 2750
[URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get:
b = [B]55[/B]

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the ave

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even?
Cost function C(b) where b is the number of bikes:
C(b) = Variable Cost + Fixed Cost
C(b) = Cost per bike * b + operating cost
C(b) = 60b + 3600
Revenue function R(b) where b is the number of bikes:
R(b) = Sale price * b
R(b) = 100b
Break Even is when Cost equals Revenue, so we set C(b) = R(b):
60b + 3600 = 100b
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]90[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is t

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal
Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass:
1.5d > 24
To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get:
[B]d > 16[/B]

A cable company charges $75 for installation plus $20 per month. Another cable company offers free i

A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same
[U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 20m + 75
[U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 35m
The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m:
20m + 75 = 35m
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]5[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the mon

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this?
to start, we have:
[LIST]
[*]Let the salesman's monthly sales be s.
[*]With a 10% discount as a decimal of 0.1
[*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality
[*]We want 10% times s + 800 per month is greater than or equal to 3200
[/LIST]
We want the inequality:
0.1s + 800 >= 3200
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get:
[B]s >= 24000[/B]

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take bef

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take before the cars value falls below $15000
Let m be the number of months.We have our Book Value B(m) given by:
B(m) = 25600 - 90m
We want to know when the Book value is less than 15,000. So we have an inequality:
25600 - 90m < 15000
Typing [URL='https://www.mathcelebrity.com/1unk.php?num=25600-90m%3C15000&pl=Solve']this inequality into our search engine and solving for m[/URL], we get:
[B]m > 117.78 or m 118 months[/B]

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m mi

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation.
Let m be the number of minutes. We have the cost equation C(m):
[B]0.25m + 12.95 = $21.20[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 ce

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes.
We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200:
[B]C(x) = 20 + 0.05(x - 200)[/B]

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 pe

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same?
Let g be the number of GB.
The limited plan has a cost as follows:
C = 10(g - 5) + 55
C = 10g - 50 + 55
C = 10g + 5
We want to set the limited plan equal to the unlimited plan and solve for g:
10g + 5 = 70
Solve for [I]g[/I] in the equation 10g + 5 = 70
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 5 and 70. To do that, we subtract 5 from both sides
10g + 5 - 5 = 70 - 5
[SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE]
10g = 65
[SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE]
10g/10 = 65/10
g = [B]6.5[/B]
Check our work for g = 6.5:
10(6.5) + 5
65 + 5
70

A cellular offers a monthly plan of $15 for 350 min. Another cellular offers a monthly plan of $20 f

A cellular offers a monthly plan of $15 for 350 min. Another cellular offers a monthly plan of $20 for 425 min. Which company offers the better plan?
Let's figure out the unit cost of minutes per dollar:
[LIST=1]
[*]Plan 1: 350 minutes / $15 = 23.33 minutes per dollar
[*]Plan 2: 425 minutes / $20 = 21.25 minutes per dollar
[/LIST]
[B]Plan 2 is better, because you get more minutes per dollar.[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute cost $.35. This month you used 750 minutes. How much do you owe?
Calculate the excess minutes over the standard plan:
Excess Minutes = 750 - 600
Excess Minutes = 150
Calculate additional cost:
150 additional minutes * 0.35 per additional minutes = $52.50
Add this to the standard plan cost of $49.99
$52.50 + $49.99 = [B]$102.49[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute costs $.35. This month you used 750 minutes. How much do you owe
[U]Find the overage minutes:[/U]
Overage Minutes = Total Minutes - Free Minutes
Overage Minutes = 750 - 600
Overage Minutes = 150
[U]Calculate overage cost:[/U]
Overage Cost = Overage Minutes * Overage cost per minute
Overage Cost = 150 * 0.35
Overage Cost = $52.5
Calculate total cost (how much do you owe):
Total Cost = Monthly Fee + Overage Cost
Total Cost = $49.99 + $52.50
Total Cost = [B]$102.49[/B]

A checking account is set up with an initial balance of $2400 and $200 are removed from the account

A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000
200 is removed, so we subtract. Let m be the number of months. We want the following equation:
[B]2400 - 200m = 1000
[/B]
Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]7[/B]

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item tha

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order?
[U]Set up Cost function C(t) where t is the number of tapestries:[/U]
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
[U]Set up Revenue function R(t) where t is the number of tapestries:[/U]
R(t) = Sale Price * number of tapestries
R(t) = 63t
[U]Set up Profit function P(t) where t is the number of tapestries:[/U]
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
[U]The problem asks for profit when t = 2400:[/U]
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = [B]43,600[/B]

a company made a profit of $4 million per month for 8 months, then lost $10 million per month for 4

a company made a profit of $4 million per month for 8 months, then lost $10 million per month for 4 months. What was their result for the year?
Profits = 4 million per month * 8 months = 32,000,000
Losses = 10 million per month * 4 months = 40,000,000
Calculate results for the year:
Result for the year = Profits - Losses
Result for the year = 32,000,000 - 40,000,000
Result for the year = [B]8,000,000[/B]

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
[U]Set up Cost function C(b) where t is the number of tapestries:[/U]
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
[U]Set up Revenue function R(b) where t is the number of tapestries:[/U]
R(b) = Sale Price * number of boats
R(b) = 75b
[U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U]
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get:
b = [B]60[/B]

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each l

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp.
Set up the Cost Equation C(l) where l is the price of each lamp:
C(l) = Variable Cost x l + Fixed Cost
C(l) = 90l + 1800
Determine the revenue function R(l)
R(l) = 150l
Determine the profit function P(l)
Profit = Revenue - Cost
P(l) = 150l - (90l + 1800)
P(l) = 150l - 90l - 1800
[B]P(l) = 60l - 1800[/B]
Determine the break even point:
Breakeven --> R(l) = C(l)
150l = 90l + 1800
[URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 wo

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 workers 6 months to build half of the road. How many additional workers must be added to finish the road in the remaining 4 months?
Calculate unit rate per one worker:
10 workers * 6 months = 60 months for one worker
Calculate workers needed:
60 months / 4 months = 15 workers
Calculate additional workers needed:
Additional workers needed = New workers needed - Original workers needed
Additional workers needed = 15 - 10
Additional workers needed = [B]5 additional workers[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate.

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate.
[U]Calculate Monthly Nominal Rate:[/U]
Monthly Nominal Rate = Annual Rate / 12 months per year
Monthly Nominal Rate = 36%/12
Monthly Nominal Rate = 3%
[U]Since there are 12 months in a year, we compound 12 times to get the effective rate below:[/U]
Effective Rate = (1 + Monthly Nominal Rate as a Decimal)^12 - 1
Since 3% = 0.03, we have:
Effective Rate = 100% * ((1 + 0.03)^12 - 1)
Effective Rate = 100% * ((1.03)^12 - 1)
Effective Rate = 100% * (1.42576088685 - 1)
Effective Rate = 100% * (0.42576088685)
Effective Rate = [B]42.58%[/B]

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represe

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal?
Let c be the number of cups. We want to know how many cups (x) where:
1.75x > 25
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.75x%3E25&pl=Show+Interval+Notation']inequality solver[/URL], we see:
[B]x > 14.28[/B]

A family is renting an apartment. For 2007, the rent is $1376 per month. The monthly rent in 2007

A family is renting an apartment. For 2007, the rent is $1376 per month. The monthly rent in 2007 is 7.5% higher than the monthly rent in 2006. Determine the monthly rent in 2006.
7.5% as a decimal is 0.075
To increase a value by 7.5%, we multiply by 1.075
[U]Calculate Rent Increase[/U]
R(2007) = R(2006) * 1.075
R(2007) = 1376 * 1.075
R(2007) = [B]1,479.20[/B]

A family of four used about 11,370 gallons of water in their home last month. There were 30 days in

A family of four used about 11,370 gallons of water in their home last month. There were 30 days in the month. About how many gallons of water did each person use each day?
11370 gallons of water / (30 days in a month * 4 people)
11370 gallons of water / (120 people days)
94.75 [B]gallons[/B]

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When doe

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card?
Subtract the sign up fee of $30 from your gift card amount:
$130 - $30 = $100
Since each month costs $20, we have $100/$20 = 5 months.
So if you go for [B]more than 5 months[/B], you'll exceed your gift card.

A gym membership has a $50 joining fee plus charges $17 a month for m months

A gym membership has a $50 joining fee plus charges $17 a month for m months
Build a cost equation C(m) where m is the number of months of membership.
C(m) = Variable Cost * variable units + Fixed Cost
C(m) = Months of membership * m + Joining Fee
Plugging in our numbers and we get:
[B]C(m) = 17m + 50
[MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus 7 cents per check. How many checks should be written each month to make the credit union a better deal?
Set up the cost function B(c) for the local bank where c is the number of checks:
B(c) = 0.03c + 19
Set up the cost function B(c) for the credit union where c is the number of checks:
B(c) = 0.07c + 7
We want to find out when:
0.07c + 7 < 0.03c + 19
[URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%2B7%3C0.03c%2B19&pl=Solve']Typing this inequality into our search engine[/URL], we get:
c < 300

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit.
The cost function for each unit u is:
C(u) = Variable Cost * Units + Fixed Cost
C(u) = 10u + 100000
The revenue function R(u) is:
R(u) = 22u
We want the break-even point, which is where:
C(u) = R(u)
10u + 100000 = 22u
[URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get:
u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit.
Let u be the number of units. We have a cost function C(u) as:
C(u) = Variable cost * u + Fixed Cost
C(u) = 14u + 100000
[U]We have a revenue function R(u) with u units as:[/U]
R(u) = Sale Price * u
R(u) = 20u
[U]We have a profit function P(u) with u units as:[/U]
Profit = Revenue - Cost
P(u) = R(u) - C(u)
P(u) = 20u - (14u + 100000)
P(u) = 20u - 14u - 100000
P(u) = 6u - 1000000

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produce

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit.
Set up cost function where u equals each unit produced:
C(u) = 7u + 25,500
Set up revenue function
R(u) = 10u
Break Even is where Cost equals Revenue
7u + 25,500 = 10u
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produce

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produced. The product sells for $13/unit.
Using our [URL='http://www.mathcelebrity.com/cost-revenue-profit-calculator.php?fc=52500&vc=8&r=13&u=20000%2C50000&pl=Calculate']cost-revenue-profit calculator[/URL], we get the following:
[LIST]
[*]P(x) = 55x - 2,500
[*]P(20,000) = 47,500
[*]P(50,000) = 197,500
[/LIST]

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age o

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have:
The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is:
[B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight.
The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have
[B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
Every month, the baby gains 2/3 of a pound. So we have:
[B]y = 2/3x + 7
[/B]
The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even?
Let the number of days be d. Break even means both costs are equal. We want to find when:
4.75d = 80
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get:
d = 16.84 days
We round up to an even [B]17 days[/B].

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the monthly charge and use d to represent data
We multiply gigabyte fee by d and add the usage fee:
[B]15d + 30[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Set up the cost equations for each plan. The cost equation for the phone plans is as follows:
Cost = Cost Per Minute * Minutes + Monthly Fee
Calculate the cost of Plan A:
Cost for A = 0.08m + 0. <-- Since there's no monthly fee
Calculate the cost of Plan B:
Cost for B = 0.07m + 1.50
The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality:
0.08m > 0.07m + 1.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]m > 150
This means Plan A costs more when you use more than 150 minutes per month.[/B]

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is 27.5 cm
We set up the height function H(m) where m is the number of months since now. We have:
H(m) = 4.5m + 15
We want to know when H(m) = 27.5, so we set our H(m) function equal to 27.5:
4.5m + 15 = 27.5
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.5m%2B15%3D27.5&pl=Solve']type this equation into our search engine[/URL] and we get:
m = 2.78
So we round up to [B]3 whole months[/B]

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance p

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance premium of $74.28 and $25 in union dues each paycheck. 1. What is their semimonthly salary?
Calculate the number of semi-monthly periods per year:
Semi-monthly periods per year = 12 Months per year * 2
Semi-monthly periods per year = 24
Calculate semi-monthly salary amount:
Semi-monthly salary amount = Annual Salary / Semi-monthly periods per year
Semi-monthly salary amount = $36,000 / 24
Semi-monthly salary amount = $1,500
Now, calculate the net pay each semimonthly period:
Net pay = Semi-monthly salary amount - Health Insurance Premium - Union Dues
Net pay = $1,500 - $74.28 - $25
Net pay = [B]$1,400.72[/B]

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni.

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have peppers. How many pizzas have pepperoni and peppers?
We multiply the pizzas sold by the percentage of pepperoni times the fraction of peppers. Since 70% is 7/10, we have:
Pizzas with pepperoni and peppers = 15,000 * 7/10 * 2/3
7/10 * 2/3 = 14/30. [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F30&frac2=3%2F8&pl=Simplify']Using our fraction simplifier calculator[/URL], we can reduce this to 7/15
Pizzas with pepperoni and peppers = 15,000 * 7/15
Pizzas with pepperoni and peppers = [B]7,000[/B]

A road construction team built a 114 mile road over a period of 19 months what was their average bui

A road construction team built a 114 mile road over a period of 19 months what was their average building distance per a month
Average building distance = miles built / months of building
Average building distance = 114/19
Average building distance = [B]6 miles per month[/B]

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. Wha

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. What did the clerk earn the month that she sold $12,800 in merchandise?
[U]Calculate Commission Sales Eligible Amount:[/U]
Commission Sales Eligible Amount = Sales - 3900
Commission Sales Eligible Amount = 12800 - 3900
Commission Sales Eligible Amount = 8900
[U]Calculate Commission Amount:[/U]
Commission Amount = Commission Sales Eligible Amount * Commission Percent
Commission Amount = [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=4&den1=8900&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']8900 * 4%[/URL]
Commission Amount = 356
[U]Calculate total earnings:[/U]
Total Earnings = Base Salary + Commission Amount
Total Earnings = 750 + 356
Total Earnings = [B]1106[/B]

a school fee is 32000 per year what is fees of one month

a school fee is 32000 per year what is fees of one month
32000 per year / 12 months per year = [B]2666.67 per month[/B]

A social networking site currently has 38,000 active members per month, but that figure is dropping

A social networking site currently has 38,000 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 7 months?
Setup an equation S(m) where m is the number of months that pass:
S(m) = 38000 * (1 - 0.05)^t
S(m) = 38000 * (0.95)^t
The problem asks for S(7):
S(7) = 38000 * (0.95)^7
S(7) = 38000 * (0.69833729609)
S(7) = 26,536.82
We round down to a full person and get:
S(7) = [B]26,536[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale?
[LIST=1]
[*]We start with 293 hats
[*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228
[*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65
[*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150
[*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B]
[/LIST]

A student posed a null hypothesis that during the month of September, the mean daily temperature of

A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0.56. Thus, he could conclude:
a. In September, Boston was colder than New York
b. In September, Boston was warmer than New York
c. He may reject the null hypothesis
d. He failed to reject the null hypothesis
[B]d. He failed to reject the null hypothesis[/B]
[I]Higher p value tells us we cannot reject the null hypothesis[/I]

A television sells for $750. Instead of paying the total amount at the time of the purchase, the sam

A television sells for $750. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $100 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase?
Option 2:
100 + 50(14)
100 + 700
800
800 - 750 = [B]$50 saved[/B]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text message

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages.
We set up the cost function C(x) where x is the number of text messages per month:
C(x) = Cost per text * x + Monthly cost
Plugging in our given numbers, we get:
[B]C(x) = 0.28x + 7[/B]

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population afte

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population after 6 years?
[LIST]
[*]1 year = 12 months
[*]12 months / 4 months = 3 compounding periods per year
[*]3 compounding periods per year * 6 years = 18 compounding periods
[/LIST]
So we have our population growth as follows:
25,000(1.077)^18
25,000 * 3.8008668804
95,021.67 ~ [B]95,021[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years.
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to [B]92,545[/B]

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
Set up a cost function C(m) where m is the number of movies you rent:
C(m) = Rental cost per movie * m + Membership Fee
[U]Video Store 1 cost function[/U]
C(m) = 1m + 7.5
Video Store 2 cost function:
C(m) = 2.50m
We want to know when the costs are the same. So we set each C(m) equal to each other:
m + 7.5 = 2.50m
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

A woman earns $2400 per month and budgets $480 per month for food. What percent of her monthly incom

A woman earns $2400 per month and budgets $480 per month for food. What percent of her monthly income is spent on food?
480/2400 using our [URL='http://www.mathcelebrity.com/perc.php?num=480&den=2400&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL] is [B]20%[/B].

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Adrienne brings home $1580 per month. She spends $316 on food. What is the fraction of what she spen

Adrienne brings home $1580 per month. She spends $316 on food. What is the fraction of what she spends on food
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=316%2F1580&frac2=3%2F8&pl=Simplify']fraction calculator[/URL], we see that:
316/1580 = [B]1/5[/B]

Allen saves $162 a month. Allen saves $43 less each month than Lane. How much will Lane save in 2 ye

Allen saves $162 a month. Allen saves $43 less each month than Lane. How much will Lane save in 2 years?
[U]Calculate Lane's monthly savings:[/U]
Lane's monthly savings = Allen's monthly savings + 43 (since Allan saves 43 less than Lane)
Lane's monthly savings = 162 + 43
Lane's monthly savings = 205
1 year = 12 months
2 years = 24 months
So we have:
Lane's savings in 2 years = Lane's monthly savings * 24 months
Lane's savings in 2 years = 205 * 24
Lane's savings in 2 years = [B]4,920[/B]

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a $53 discount her discounted bill at the end of the year was 463 what is her monthly fee
Her full annual bill is found by adding the discounted annual bill to the discount amount:
Full annual bill = Discounted annual bill + discount amount
Full annual bill = 463 + 53
Full annual bill = 516
Her monthly gym membership is found by the following calculation:
Monthly Gym Membership = Full Annual Bill / 12
Monthly Gym Membership = 516 / 12
Monthly Gym Membership = [B]$43[/B]

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the en

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month?
We set up the cost function C(m) where m is the number of months of membership:
C(m) = cost per month * m + joining fee
Plugging in our numbers from the problem with 12 months in a year, we get:
12c + 35 = 299
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]22[/B]

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. I

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. If she earns a total of 87400 dollars per year, what is her monthly salary in dollars?
Calculate the annual salary without bonus:
Annual Salary = Total Pay - Christmas Bonus
Annual Salary = 87400 - 6400
Annual Salary = 81000
Now calculate the monthly salary. [I]Note: there are 12 months in a year[/I]:
Monthly Salary = Annual Salary / 12
Monthly Salary = 81000/12
[URL='https://www.mathcelebrity.com/fraction.php?frac1=81000%2F12&frac2=3%2F8&pl=Simplify']Monthly Salary[/URL] = [B]6750[/B]

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play.
Let s be the cost of software packages and m be the months of game play. We have:
[LIST]
[*]Angie: 2s + 4m
[*]Kenny: s + m
[/LIST]
We are given each software package costs $25. So the revised equations above become:
[LIST]
[*]Angie: 2(25) + 4m = 50 + 4m
[*]Kenny: 25 + m
[/LIST]
Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together:
4m + 50 + 25 + m = 155
Combine like terms:
5m + 75 = 155
[URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how m

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest?
Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following:
[LIST=1]
[*]Accumulated Value After 7 years = [B]$101,086.45[/B]
[*]Principal = 79,800
[*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B]
[/LIST]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum am

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month.
Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when:
0.20s + 600 >= 1500
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get:
s >= [B]4500[/B]

At Zabowood’s Gadget Store, some items are paid on instalment basis through credit cards. Clariza wa

[B]A[/B]t Zabowood’s Gadget Store, some items are paid on instalment basis through credit cards. Clariza was able to sell 10 cellphones costing Php 18,000.00 each. Each transaction is payable in 6 months equally divided into 6 equal instalments without interest. Clariza gets 2% commission on the first month for each of the 10 cellphones. Commission decreases by 0.30% every month thereafter and computed on the outstanding balance for the month. How much commission does Clariza receive on the third month?
Calculate Total Sales Amount:
Calculate Total Sales Amount = 10 cellphones * 18000 per cellphone
Calculate Total Sales Amount = 180000
Calculate monthly sales amount installment:
monthly sales amount installment = Total Sales Amount / 6
monthly sales amount installment = 180000/6
monthly sales amount installment = 30000 per month
Calculate Third Month Commission:
Third month commission = First Month Commission - 0.30% - 0.30%
Third month Commission = 2% - 0.30% - 0.30% = 1.4%
Calculate 3rd month commission amount:
3rd month Commission amount = 1.4% * 30000
3rd month Commission amount = [B]420[/B]

Austin deposited $4000 into an account with 4.8% interest,compounded monthly. Assuming that no

Austin deposited $4000 into an account with 4.8% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 4 years? Do not round any intermediate computations, and round your answer to the nearest cent.
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=40000&nval=4&int=4.8&pl=Annually']balance calculator[/URL], we get:
[B]$48,250.87[/B]

Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used

Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used $36.50 every month to pay for art lessons. After 10 months, he used 1/2 of the total money left in his account to go to a summer camp for artists. What is the total amount of money Benny spent to go to the summer camp?
If Benny deposits $92.50 every month and withdraws $36.50 every month, his net deposit each month is:
92.50 - 36.50 = 56
Benny does this for 10 months, so his balance after 10 months is:
56 * 10 = 560
Half of this is:
560/2 = [B]280[/B]

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy.

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month.
Let x equal to the number room movie rentals per month. Our inequality is:
120 + 2.99x < 150
To solve for the number of movies, Add 120 to each side
2.99x < 30
Divide each side by 2.99
x < 10.03, which means 10 since you cannot buy a fraction of a movie

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month
Let Bud's earnings be b.
Let Maxine's earnings be m.
We're given two equations:
[LIST=1]
[*]b = m + 400
[*]b + m = 3600
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for b
m + 400 + m = 3600
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B400%2Bm%3D3600&pl=Solve']type it in our search engine[/URL] and we get:
m = 1600
To solve for b, we substitute m = 1600 into equation (1) above:
b = 1600 + 400
b = [B]2200[/B]

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a. In how many months will both gym memberships cost the same? What will that cost be?
Set up cost equations where m is the number of months enrolled:
[LIST=1]
[*]C(m) = 35m + 150
[*]C(m) = 60m
[/LIST]
Set them equal to each other:
35m + 150 = 60m
[URL='http://www.mathcelebrity.com/1unk.php?num=35m%2B150%3D60m&pl=Solve']Pasting the equation above into our search engine[/URL], we get [B]m = 6[/B].

Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signe

Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signed the lease. In total, they paid $1,850. What is the rent for one month? Write an equation and solve it.
Equation, let m = rent for one month
3m + 200 = 1,850
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3m%2B200%3D1850&pl=Solve']Equation Solver[/URL], we get [B]m = 550[/B].

Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.0

Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.01 per copy. For which number of copies do the two companies charge the same amount?
With c as the number of copies, we have:
Company A Cost = 300 + 0.05c
Company B Cost = 600 + 0.01c
Set them equal to each other
300 + 0.05c = 600 + 0.01c
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=300%2B0.05c%3D600%2B0.01c&pl=Solve']equation solver[/URL] to get:
[B]c = 7,500[/B]

Compound Interest Accumulated Balance

Given an interest rate per annum compounded annually (i), semi-annually, quarterly, monthly, semi-monthly, weekly, and daily, this calculates the accumulated balance after (n) periods

Credit Card Balance

This calculator shows 3 methods for paying off a credit card balance on a monthly installment basis given an outstanding balance and an Annual Percentage Rate (APR):

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

1) Minimum Payment Amount

2) Minimum Percentage Amount

3) Payoff in Years

Date and Time Difference

Calculates the difference between two dates using the following methods

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

Date Calendar

Shows a calendar for a month and year

Date Information

This calculator takes a date in mm/dd/yyyy format, and gives the following information about it:

* Weekday

* Day number in the year

* Week number in the year

* Number of days in the month containing that date

* Leap Year (Yes or No)

* Zodiac Sign

* Julian Date

* Weekday

* Day number in the year

* Week number in the year

* Number of days in the month containing that date

* Leap Year (Yes or No)

* Zodiac Sign

* Julian Date

Dave has a savings account that pays interest at 3 1/2% per year. His opening balance for May was $1

Dave has a savings account that pays interest at 3 1/2% per year. His opening balance for May was $1374.67. He did not deposit or withdraw money during the month. The interest is calculated daily. How much interest did the account earn in May?
First, determine n, which is 31, since May has 31 days.
We use our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1374.67&nval=31&int=3.5&pl=Daily']compound interest balance calculator[/URL] to get:
[B]1,378.76[/B]

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up

Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money?
We set up a balance equation B(m) where m is the number of months.
[U]Set up Deon's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m
[U]Set up Mai's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m
When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m
Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m
[SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE]
25m + 650 = 850
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650
[SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE]
25m = 200
[SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE]
25m/25 = 200/25
m = [B]8[/B]

Ed invests $5,500 into the stock market which earns 2% per year. In 20 years, how much will Ed's inv

Ed invests $5,500 into the stock market which earns 2% per year. In 20 years, how much will Ed's investment be worth if interest is compounded monthly? Round to the nearest dollar.
20 years * 12 months per year = 240 months
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5550&nval=240&int=2&pl=Monthly']compound interest calculator[/URL], we get:
[B]8,276.87[/B]

Effective Annual Yield Rate

Figures out the effective annual yield rate of interest entered by compounding daily, weekly, semi-monthly, monthly, quarterly, semi-annually, and continuously.

Emil bought a camera for $268.26, including tax. He made a down payment of $12.00 and paid the balan

Emil bought a camera for $268.26, including tax. He made a down payment of $12.00 and paid the balance in 6 equal monthly payments. What was Emil’s monthly payment for this camera?
Calculate remaining balance
268.26 - 12 = 256.26
Determine monthly payment:
256.26/6 = [B]21.36[/B]

Find Necessary Sample Size

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minu

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minute of use. The least she has been charged in a month is $86.04 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Maya's cost function is C(m), where m is the number of minutes used.
C(m) = 0.04m + 27
We are given C(m) = $86.04. We want her cost function [I]less than or equal[/I] to this.
0.04m + 27 <= 86.04
[URL='https://www.mathcelebrity.com/1unk.php?num=0.04m%2B27%3C%3D86.04&pl=Solve']Type this inequality into our search engine[/URL], and we get [B]m <= 1476[/B].

Fred earns $420 a month. If his monthly car payment is one quarter of his pay, how much is his car p

Fred earns $420 a month. If his monthly car payment is one quarter of his pay, how much is his car payment?
1/4 means divided by 4, so we have:
Monthly Payment = Earnings/4
Monthly Payment =420/4
Monthly Payment = [B]$105[/B]

Free Trial to Audible

Use this link to get 3 free months on Audible:
[URL]https://www.audible.com/pd/B0B4TVPRMV/?source_code=AUDFPWS0223189MWT-BK-ACX0-313125&ref=acx_bty_BK_ACX0_313125_rh_us[/URL]

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How ma

Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How many hours of lessons per month must he give to earn a profit of $326?
Build a profit function P(h) where h is the number of hours:
P(h) = Hourly Rate * Number of Hours (h) - Cost of Piano
P(h) = 15h - 49
The problem asks for the number of hours where P(h) = $326
15h - 49 = 326
We take this equation and [URL='https://www.mathcelebrity.com/1unk.php?num=15h-49%3D326&pl=Solve']type it in our search engine[/URL] to solve for h:
h = [B]25[/B]

Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this

Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this information.
Let m be the number of months Georgie uses the gym. Our equation G(m) is the cost Georgie pays for m months.
G(m) = Variable Cost * m (months) + Fixed Cost
Plug in our numbers:
[B]G(m) = 15m + 25[/B]

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal.
Gym A cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 35m + 75
Gym B cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 60m
Set them equal to each other:
35m + 75 = 60m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=35m%2B75%3D60m&pl=Solve']we type this equation into our search engine[/URL] and get:
m = [B]3[/B]

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earn

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earns 2.0% commission on sales each month. This month she had $131600 in sales. What was harjaps gross income for this month?
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
[U]Calculate Monthly Base Salary:[/U]
Monthly Base Salary = Weekly Base Salary * 4
Monthly Base Salary = $420 * 4
Monthly Base Salary = $1,680
[U]Calculate Commissions:[/U]
Commissions = Sales * Commission Percent
Commissions = $131,600 * 2%
Since 2% as a decimal is 0.02, we have:
Commissions = $131,600 * 0.02
Commissions = $2,632
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
Gross Income = $1,680 + $2632
Gross Income = [B]$4,312[/B]

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

How much money would you have after 4 years if you invested $550 at 7% annual interest, compounded m

How much money would you have after 4 years if you invested $550 at 7% annual interest, compounded monthly?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=550&nval=48&int=7.00&pl=Monthly']compound interest calculator, with 4 years * 12 months per year = 48 months as n[/URL], we get:
[B]727.13[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 10 yea

How much would you need to deposit in an account now in order to have $6000 in the account in 10 years? Assume the account earns 6% interest compounded monthly.
We start with a balance of B. We want to know:
B(1.06)^10 = 6000
B(1.79084769654) = 6000
Divide each side of the equation by 1.79084769654 to solve for B
B = [B]3,350.37[/B]

How much would you need to deposit in an account now in order to have $6000 in the account in 15 yea

How much would you need to deposit in an account now in order to have $6000 in the account in 15 years? Assume the account earns 8% interest compounded monthly.
8% compounded monthly = 8/12 = 0.6667% per month.
15 years = 15*12 = 180 months
We want to know an initial balance B such that:
B(1.00667)^180 = $6,000
3.306921B = $6,000
Divide each side by 3.306921
[B]B = $1,814.38[/B]

I have $789 in the bank and make 1% interest a month. How much money do I have at the end of 6 month

I have $789 in the bank and make 1% interest a month. How much money do I have at the end of 6 months?
Our balance is found using our compound interest formula:
New Balance = Starting Balance * (1 + i/100)^t
With I = 1% and t = 6, we have:
New Balance = 789 * (1 + 1/100)^6
New Balance = 789 * (1.01)^6
New Balance = 789 * 1.0615201506
New Balance = [B]837.54[/B]

I need help for this question. Can someone pls help me?

The simple interests earned on the sum of money for 4 years at 7.5% p.a. exceeds that on the same sum for 3.5 years at 8% p.a. by $90.
(a)Find the original sum of money.
(b)If the original sum of money accumulates to $4612.50 in 5 months at simple interest, find the interests rate per annum.

I play volleyball 3 days a week for 2 hours how many hours do I play per month?

I play volleyball 3 days a week for 2 hours how many hours do I play per month?
2 hours per day * 3 days per week * 4 weeks in a month = [B]24 hours per month[/B]

if $7000 is invested at 3% compounded monthly, what is the amount after 4 years

if $7000 is invested at 3% compounded monthly, what is the amount after 4 years
4 years = 12 *4 = 48 months since we're compounding monthly.
From our c[URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=48&int=3&pl=Monthly']ompound interest calculator,[/URL] we get:
[B]$3,381.98[/B]

if a city grows by 12% per month what is the yearly growth rate

if a city grows by 12% per month what is the yearly growth rate
We know that there are 12 months in a year.
12% = 0.12
Annual Growth Rate = (1 + Monthly Growth Rate)^12 - 1
Annual Growth Rate = (1 + 0.12)^12 - 1
Annual Growth Rate = (1.12)^12 - 1
Annual Growth Rate = 3.89597599255 - 1
Annual Growth Rate = 2.90
For our percentage, our annual growth rate is the Annual growth rate * 100%
2.90 * 100% = [B]290%[/B]

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his total savings after 10 months?
Set up the savings function S(m), where m is the number of months and I is the interest rate growth:
S(m) = Initial Amount * (1 + i)^m
Plugging in our number at m = 10 months we get:
S(10) = 750 * (1 + 0.08)^10
S(10) = 750 * 1.08^10
S(10) = [B]$1,619.19[/B]

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal in

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
[U]Determine the monthly payment[/U]
The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL]
[U]Determine the total payments made[/U]
Total payment is 36 times $114.87 = $4,135.37
[U]Now determine the total interest paid[/U]
Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you save $110 in one month, how much will you save in one year?

If you save $110 in one month, how much will you save in one year?
110 per month * 12 months in a year = [B]1,320 saved in a year[/B]

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March i

in a city, the record monthly high temperature for March is 56°F. The record monthly low for March is -4°F. What is the range of temperatures for the month of March
Range = High - Low
Range = 56 - -4
Range = 56 + 4 [I]since double negative is positive[/I]
Range = [B]60[/B]

James wants to save $1500 for a summer trip. Summer is about 6 months away. How much money will Jame

James wants to save $1500 for a summer trip. Summer is about 6 months away. How much money will James have to save per month
$1500/6 months = [B]250 per month[/B]

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula

Janice is looking to buy a vacation home for $185,000 near her favorite southern beach. The formula to compute a mortgage payment, M, is shown below, where P is the principal amount of the loan, r is the monthly interest rate, and N is the number of monthly payments. Janice's bank offers a monthly interest rate of 0.325% for a 12-year mortgage. How many monthly payments must Janice make?
12 years * 12 months per year = [B]144 mortgage payments[/B]

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amou

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amount E. Write an expression to show how much he earned per day in a month. Suppose he is working for 20 days per month.
[LIST=1]
[*]Each day, Jay earns a profit of S - E.
[*]For one month (30 days), he earns 30(S - E)
[*]For 20 working days in a month, he earns 20(S - E)
[/LIST]

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did

Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with?
Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below:
s + 150 = 500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 3[B]50[/B]

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?

Jerry, an electrician, worked 7 months out the year. What percent of the year did he work?
We know that there are 12 months in a year.
Percentage worked = Months worked in a year / months in a year * 100%
Percentage worked = 7/12 * 100%
Percentage worked = 0.5833333 * 100%
Multiplying by 100 means we shift the decimal place 2 spaces to the right:
Percentage worked = [B]58.33%[/B]

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation?
Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis.
[LIST=1]
[*]Month 1 = (1, 18)
[*]Month 2 = (2, 20)
[*]Month 3 = (3, 22)
[*]Month 4 = (4, 24)
[/LIST]
You can see for every 1 unit move in x, we get a 2 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=22&slope=+2%2F5&xtwo=4&ytwo=24&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = [B]2[/B]

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sal

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n that he will watch in m months
Build movie equation. 3 movies per month at m months means we multiply:
[B]n = 3m[/B]

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]

Josh currently bench presses 150 lbs. He increases that amount by 10% a month for 3 months. About ho

Josh currently bench presses 150 lbs. He increases that amount by 10% a month for 3 months. About how much can he bench press now?
We have 150(1.1)^3. We can also write this as 150(1.1)(1.1)(1.1).
The 10% compounds. After 3 months, Josh benches 199.65 lbs, or approximately 200 lbs.

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of sla

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat?
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
[LIST=1]
[*]4s + p = 11.45
[*]5s + 3p + c = 27.41
[*]5s + c = 16.94
[/LIST]
Rearrange (1) by subtracting 4s from each side:
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get:
[B]s = 1.99 [/B] <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
[B]p = 3.49[/B] <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
[B]c = 6.99[/B] <-- Sports Coat cost

Kent Realty Company had an annual loss of $63,408. What was the average loss per month?

Kent Realty Company had an annual loss of $63,408. What was the average loss per month?
Convert years to months
1 year = 12 months
63,408/12 = [B]5,284 per month[/B]

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much

Kevin borrowed $8000 at a rate of 7.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 10 years?
We want to find 8,000(1.075)^10
Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=10&int=7.5&pl=Annually']balance calculator[/URL], we get:
[B]$16,488.25[/B]

Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4

Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4 spaces were added to each row. If the lot has 8 rows, how many spaces are there now?
23 spaces + 4 additional spaces = 27 spaces
27 spaces * 8 rows = [B]216 spaces[/B]

Last month, my saving account was balance was $1,000. since then, i spent x dollars from my saving

Last month, my saving account was balance was $1,000. since then, i spent x dollars from my saving
Spending means reducing our balance, so we have a new balance of:
[B]1000 - x[/B]

Last year, Susan interviewed 240 people. How many each month?

Last year, Susan interviewed 240 people. How many each month?
240 people / yr * 1 yr / 12 months = 240 people / 12 months = [B]20 people per month[/B]

Lauren invested $340 in an account paying an interest rate of 5.8% compounded monthly. Assuming no d

Lauren invested $340 in an account paying an interest rate of 5.8% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?
13 years * 12 months per year = 156 compounding periods.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=340&nval=156&int=5.8&pl=Monthly']Using our compound interest balance calculator[/URL] with 156 for t, we get:
$[B]721.35[/B]

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI

Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte.
Operating Fee charge per Mb
CIVSIN 29.95 0.14
GOMI 4.95 0.39
(i) Write down a system of equations to model the above situation
(ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans?
(i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.14m + 29.95[/B]
Set up a cost function C(m) for GOMI where m is the number of megabytes used:
C(m) = charge per Mb * m + Operating Fee
[B]C(m) = 0.39m + 4.95
[/B]
(ii) At how many Mb is the monthly cost the same?
Set both cost functions equal to each other:
0.14m + 29.95 = 0.39m + 4.95
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]100[/B]
(ii) What is the equal monthly cost of the two plans?
CIVSIN - We want C(100) from above where m = 100
C(100) = 0.14(100) + 29.95
C(100) = 14 + 29.95
C(100) = [B]43.95[/B]
GOMI - We want C(100) from above where m = 100
C(100) = 0.39(100) + 4.95
C(100) = 39 + 4.95
C(100) = [B]43.95[/B]

Lino worked in Singapore for 60 months How many years did he work in Singapore?

Lino worked in Singapore for 60 months How many years did he work in Singapore?
60 months / 12 months per year = [B]5 years[/B]

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all s

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000
Let the Sales amount be s. We have:
Sales over 1,500 is written as s - 1500
11% is also 0.11 as a decimal, so we have:
0.11(s - 1500) + 650 = 3000
Multiply through:
0.11s - 165 + 650 = 3500
0.11s + 485 = 3500
To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=0.11s%2B485%3D3500&pl=Solve']we type it in our search engine[/URL] and we get:
s = [B]27,409.10[/B]

Manuel can pay for his car insurance on a monthly basis, but if he pays an entire year's insurance i

Manuel can pay for his car insurance on a monthly basis, but if he pays an entire year's insurance in advance, he'll receive a $40 discount. His discounted bill for the year would then be $632. What is the monthly fee for his insurance?
His full bill F, is denoted as:
F - 40 = 632
[URL='https://www.mathcelebrity.com/1unk.php?num=f-40%3D632&pl=Solve']If we add 40 to each side[/URL], we get:
F = [B]$672[/B]

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking ac

Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain
Set up the Balance account B(m), where m is the number of months since the deposit.
Matt:
B(m) = 20m + 100
Ben:
B(m) = 80 + 30m
Set both balance equations equal to each other to see if they ever have the same balance:
20m + 100 = 80 + 30m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B100%3D80%2B30m&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = [B]2
So yes, they will have the same balance at m = 2[/B]

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay

Matthew's pay increases by 20% each month. If his first pay is $450, determine the amount of his pay in month 5.
Let me be the number of months. We have a pay functionalists P(m) as:
P(m) = Initial Pay * (1 + Increase %/100)^m
With m = 5, initial pay = 450, and Increase % = 20, we have
P(5) = 450 * (1.2)^5
P(5) = 450 * 2.48832
P(5) = [B]1,119.74[/B]

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c

Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Number of movies equals movies per month times the number of months. So we have:
[B]n = 2m[/B]

Months with 31 days as set M

Months with 31 days as set M
Our cardinality of this set is 7, as show below:
{[B]January, March, May, July, August, October, December[/B]}

Mortgage

Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a __standard__ or __interest only__ home or car loan with fixed interest rate. Handles amortized loans.

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5

Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app.
Set up the cost function C(m) where m is the number of months you subscribe:
C(m) = Monthly Subscription Fee * months + Purchase fee
[B]C(m) = 2.99m + 5[/B]

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets

Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets 2 more every month. After how many months will Mr. Demerath have at least 65 Hawaiian shirts?
We set up the function H(m) where m is the number of months that goes by. Mr. Demerath's shirts are found by:
H(m) = 2m + 42
The problem asks for m when H(m) = 65. So we set H(m) = 65:
2m + 42 = 65
To solve this equation for m, we[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2B42%3D65&pl=Solve'] type it in our search engine [/URL]and we get:
m = [B]11.5[/B]

Mr. Johnson earned $16,000 in 4 months. At this rate, how much money did he earn in one year?

Mr. Johnson earned $16,000 in 4 months. At this rate, how much money did he earn in one year?
$16,000 / 4 months * 12 months / year = [B]$48,000 per year[/B]

My dad’s annual income is $8460. What is the monthly income of my dad?

My dad’s annual income is $8460. What is the monthly income of my dad?
Monthly Income = Annual Income / 12
Monthly Income = 8460/12
Monthly Income = [B]$705[/B]

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise m

My rent was 800.00 a month. My landlord raised my rent to 1,240.00. What percentage did he raise my rent?.
First, calculate the difference between the old and new rent:
Difference = 1,240 - 800 = 440
Percentage increase = 440/800
[URL='https://www.mathcelebrity.com/perc.php?num=440&den=800&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Type 440/800 into the search engine, and choose the percent option[/URL]
You get [B]55%[/B] increase.

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars nandita earned last month by babysitting.
We know that:
Babysitting + Card Sales = Total earnings
Set up the equation where x is the dollars earned from babysitting:
[B]x + 28 = 224[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B28%3D224&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]196[/B]

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer w

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer would give her $10,200 plus a prize pig.
After working for 5 months, Natalie decided to quit. The farmer determined that 5 months of work was equal to $3375 plus the pig. How much money was the pig worth?
The value of a year's work is $10,200 plus a pig of unknown value. The farmer took away $6825 because Natalie worked 5 months. If Natalie worked 7 more months, she would have been paid the additional $6825.
6825/7 months work = $975 per month
A full year's work is $975 * 12 = $11,700
Pig value = Full years work - payout
Pig value = 11,700 - 10,200
Pig value = [B]1,500[/B]

Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise.

Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise. Job B pays 24,000 a year with a $500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A?
Nia Job A salary at time t: S(t)
$2,000 per month equals $24,000 per year.
So we have S(t) = 24,000(1.o2)^t
Nia Job B salary at time t: S(t)
$24,000 per year.
So we have S(t) = 24,000 + 500t
We want to know t when Job A salary is greater than Job B Salary:
24,000(1.o2)^t > 24,000 + 500t
Time | A | B
0 | 24000 | 24000
1 | 24480 | 24500
2 | 24969.6 | 25000
3 | 25468.99 | 25500
4 | 25978.37 | 26000
5 | 26497.94 | 26500
6 | 27027.9 | 27000
7 | 27568.46 | 27500
8 | 28119.83 | 28000
9 | 28682.22 | 28500
10 | 29255.87 | 29000
11 | 29840.98 | 29500
12 | 30437.8 | 30000
13 | 31046.56 | 30500

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000?

Oliver invests $1,000 at a fixed rate of 7% compounded monthly, when will his account reach $10,000?
7% monthly is:
0.07/12 = .00583
So we have:
1000(1 + .00583)^m = 10000
divide each side by 1000;
(1.00583)^m = 10
Take the natural log of both sides;
LN (1.00583)^m = LN(10)
Use the identity for natural logs and exponents:
m * LN (1.00583) = 2.30258509299
0.00252458479m = 2.30258509299
m = 912.064867899
Round up to [B]913 months[/B]

Paul spent 14 of his monthly salary for rent and 17 of his monthly salary for his credit card bill.

Paul spent 14 of his monthly salary for rent and 17 of his monthly salary for his credit card bill. If $714 was left, what was his monthly salary?
We add his left over amount + rent + credit card to get his original salary:
Original Salary = 714 + 14 + 17
Original Salary = [B]$745[/B]

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activatio

Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone.
Let m be the number of months. Our equation is:
[B]40m + 75 = 500 [/B] <-- This is the equation
[URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get:
m = [B]10.625[/B]
Since it's complete months, it would be 10 months.

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how muc

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how much will she owe after 4 years?
[U]Convert annual amounts to monthly[/U]
4 years = 12 * 4 = 48 months
i = .105/12 = 0.00875 monthly
[U]Build our accumulation function A(t) where t is the time in months[/U]
A(48) = 8,000 * (1.00875)^48
A(48) = 8,000 * 1.5192
A(48) = [B]12,153.60
[/B]
[URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=48&int=10.5&pl=Monthly']You can also use the balance calculator[/URL]

Richard earns $2700 a month. He received a 3% raise. What is Richard's new annual salary? Remember 1

Richard earns $2700 a month. He received a 3% raise. What is Richard's new annual salary? Remember 12 months in 1 year
$2,700 per month * 12 months = 32,400 per year.
A 3% raise means the new salary is:
32,400 * 1.03 = [B]$33,372[/B]

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the same rate, how many books will he sell during the month of May?
Set up a proportion of days to books where n is the number of books sold in May:
22/31 = 75/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=22&num2=75&den1=31&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] and rounding to the next integer, we get:
n = [B]106[/B]

Salary Converter

This calculator converts an annual salary to the following measures:

* Monthly

* Weekly

* Daily

* Hourly

* Each Minute

* Each Second

* Monthly

* Weekly

* Daily

* Hourly

* Each Minute

* Each Second

Sally earns an annual salary of $52,000. How does sally “gross” in one month ?

Sally earns an annual salary of $52,000. How does sally “gross” in one month?
Monthly Salary = Annual Salary / 12
Monthly Salary = 52000 / 12
Monthly Salary = [B]$4333.33[/B]

Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. w

Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. whats is the equation.
Let S(c) be the equation for the money Sarah makes selling (c) cookies. We have:
S(c) = Cost per cookies * c cookies + Base Salary
[B]S(c) = 50c + 500[/B]

Social Security and Covered Compensation

Calculates an estimated monthly Social Security Benefit based on a smooth estimate of pay over your work history.

Also calculates a covered compensation amount based on a year of birth

Also calculates a covered compensation amount based on a year of birth

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in 4 years?
[U]Calculate savings amount per month:[/U]
Savings amount per month = Earnings - Spend
Savings amount per month = 1160 - 540
Savings amount per month = 620
[U]Convert years to months[/U]
4 years = 12 * 4 months
4 years = 48 months
[U]Calculate total savings:[/U]
Total Savings = Savings per month * number of months saved
Total Savings = 620 * 48
Total Savings = [B]$29,760
[MEDIA=youtube]sbzRra8dSFs[/MEDIA][/B]

Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the

Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the last couple months. So far, Stephanie has won 8 out the total 18 games that they have played. if Stephanie wishes to have an 80% winning record, how many games in a row will Stephanie have to win, without losing?
Track each game the percentage
[LIST=1]
[*]8 out of 18 = 44.44%
[*]9 out of 19 = 47.37%
[*]10 out of 20 = 50%
[*]11 out of 21 = 52.38%
[*]12 out of 22 = 54.55%
[*]13 out of 23 = 56.52%
[*]14 out of 24 = 58.33%
[*]15 out of 25 = 60%
[*]16 out of 26 = 61.54%
[*]17 out of 27 = 62.96%
[*]18 out of 28 = 64.29%
[*]19 out of 29 = 65.52%
[*]20 out of 30 = 66.67%
[*]21 out of 31 = 67.74%
[*]22 out of 32 = 68.75%
[*]23 out of 33 = 69.7%
[*]24 out of 34 = 70.59%
[*]25 out of 35 = 71.43%
[*]26 out of 36 = 72.22%
[*]27 out of 37 = 72.97%
[*]28 out of 38 = 73.68%
[*]29 out of 39 = 74.36%
[*]30 out of 40 = 75%
[*]31 out of 41 = 75.61%
[*]32 out of 42 = 76.19%
[*]33 out of 43 = 76.74%
[*]34 out of 44 = 77.27%
[*]35 out of 45 = 77.78%
[*]36 out of 46 = 78.26%
[*]37 out of 47 = 78.72%
[*]38 out of 48 = 79.17%
[*]39 out of 49 = 79.59%
[*][B]40 out of 50 = 80%[/B]
[/LIST]
[B]So our answer is 32 games in a row[/B]

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how m

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165?
[U]Let the number of months be m. We have a total spend T of:[/U]
cost per month * m + one-time membership fee = T
[U]Plugging in our numbers, we get:[/U]
14m + 25 = 165
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]10[/B]

Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded monthly. Find the acc

Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded monthly. Find the account balance after 12 years. Round your answer to two decimal places.
Using our[URL='https://www.mathcelebrity.com/compoundint.php?bal=1000&nval=12&int=7.2&pl=Monthly'] compound interest balance calculator[/URL], we get:
[B]$1,074.42[/B]

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a c

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]

The buyer of a lot pays P10,000 every month for 10 years. If the money is 8% compounded annually, ho

The buyer of a lot pays P10,000 every month for 10 years. If the money is 8% compounded annually, how much is the cash value of the lot? (use j= 0.006434, n=120)
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=10000&nval=120&int=8&pl=Monthly']compound interest calculator[/URL], we get:
[B]22,196.40[/B]

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The seco

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal?
Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use
C(m) = 0.14m + 14
Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use
C(m) = 0.10m + 21
Set them equal to each other:
0.14m + 14 = 0.10m + 21
[URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]175[/B]

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The monthly earnings of a group of business students are are normally distributed with a standard de

The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.

The monthly rental for an apartment is $412.50. How much would the rent be for one year?

The monthly rental for an apartment is $412.50. How much would the rent be for one year?
Since there are 12 months in a year, we have:
Yearly Rent = Monthly Rent * 12
Yearly Rent = $412.50 * 12
Yearly Rent = [B]$4,950[/B]

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to rent?
Rent Payment Fraction = Rent Payment / Total Income
Rent Payment Fraction = 1600 / 3840
Our greatest common factor of 1600 and 3840 is 320.
So if we divide 1600 and 3840 by 320, we get:
Rent Payment Fraction = [B]5/12
[MEDIA=youtube]DsXk6AKT18M[/MEDIA][/B]

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company

The phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal?
Minutes Rachel talks = m
Current plan cost = 0.12m
New plan cost = 0.005m + 46
Set new plan equal to current plan:
0.005m + 46 = 0.12m
Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides
0.005m + 46 - 0.12m = 0.12m - 0.12m
[SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE]
-0.115m + 46 = 0
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 46 and 0. To do that, we subtract 46 from both sides
-0.115m + 46 - 46 = 0 - 46
[SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE]
-0.115m = -46
[SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE]
-0.115m/-0.115 = -46/-0.115
m = [B]400
She must talk over 400 minutes for the new plan to be a better deal
[URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]

The set of months of a year ending with the letters “ber”.

The set of months of a year ending with the letters “ber”.
We build set S below:
[B]S = {September, October, November, December}[/B]
The cardinality of S, denoted |S|, is the number of items in S:
[B]|S| = 4[/B]

The set of months that contain less than 30 days

The set of months that contain less than 30 days.
Let M be the set. Only February has less than 30 days out of the 12 months.
[B]M = {February}[/B]

The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representi

The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representing the value of the stock v in any month m.
Set up our equation v(m):
[B]v(m) = 0.07 + 0.02m[/B]

Time Conversions

Converts units of time between:

* nanoseconds

* microseconds

* milliseconds

* centiseconds

* kiloseconds

* seconds

* minutes

* hours

* days

* weeks

* fortnights

* months

* quarters

* years

* decades

* centurys

* milleniums

converting minutes to hours

* nanoseconds

* microseconds

* milliseconds

* centiseconds

* kiloseconds

* seconds

* minutes

* hours

* days

* weeks

* fortnights

* months

* quarters

* years

* decades

* centurys

* milleniums

converting minutes to hours

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym?
The cost function C(m) where m is the number of months for the gym membership is:
C(m) = 30m + 60
We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member.
With C(m) = 210, we have:
30m + 60 =210
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30m%2B60%3D210&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

To buy a minivan you can pay $12,500 cash or put down $5000 and make 24 monthly payments of $698.05.

To buy a minivan you can pay $12,500 cash or put down $5000 and make 24 monthly payments of $698.05. How much would you save by paying cash?
[U]Calculate the total amount with payments:[/U]
Total Amount with payments = Payment Amount * Total Payments
Total Amount with payments = $698.05 * 24
Total Amount with payments = $16,753.20
[U]Calculate the total amount saved by paying cash:[/U]
Savings by paying cash = Total Amount with payments - Cash Payment
Savings by paying cash = $16,753.20 - $12,500
Savings by paying cash = [B]$4,253.20[/B]

Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his

Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his collection while Nita is adding 4 CDs a month to her collection. Find the number of months after which they will have the same number of CDs?
Set up growth equations for the CDs where c = number of cds after m months
Tom: c = 21 + 3m
Nita: c = 14 + 4m
Set the c equations equal to each other
21 + 3m = 14 + 4m
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=21%2B3m%3D14%2B4m&pl=Solve']equation calculator[/URL], we get [B]m = 7[/B]

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500?
Let total sales be s. We're given the following earnings equation:
0.03s + 2250 = 4500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]75,000[/B]

Two years of local internet service costs 685, including the installation fee of 85. What is the mon

Two years of local internet service costs 685, including the installation fee of 85. What is the monthly fee?
Subtract the installation fee of 85 from the total cost of 685 to get the service cost only:
685 - 85 = 600
Now, divide that by 24 months in 2 years to get a per month fee
600/24 = [B]25 per month[/B]

What is the probability that a month chosen at random has less than 31 days?

What is the probability that a month chosen at random has less than 31 days?
Months with 31 days:
[LIST=1]
[*]January
[*]March
[*]May
[*]July
[*]August
[*]October
[*]December
[/LIST]
7 months out of 12 have 31 days, so our probability is [B]7/12[/B]

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for inter

You borrowed $25 from your friend. You paid him back in full after 6 months. He charged $2 for interest. What was the annual simple interest rate that he charged you? Use the formula: I = Prt.
We have I = 2, P = 25, t = 0.5
2 = 25(r)0.5
Divide each side by 0.5
4 = 25r
Divide each side by 25
r = 4/25
[B]r = 0.16[/B]
As a percentage, this is [B]16%[/B]

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long

You can afford monthly deposits of $270 into an account that pays 3.0% compounded monthly. How long will it be until you have $11,100 to buy a boat. Round to the next higher month.
[U]Set up our accumulation expression:[/U]
270(1.03)^n = 11100
1.03^n = 41.1111111
[U]Take the natural log of both sides[/U]
n * Ln(1.03) = 41.1111111
n = 3.71627843/0.0295588
n = 125.72 so round up to [B]126[/B]

You deposit $1600 in a bank account. Find the balance after 3 years if the account pays 1.75% annual

You deposit $1600 in a bank account. Find the balance after 3 years if the account pays 1.75% annual interest compounded monthly
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=1600&nval=36&int=1.75&pl=Monthly']compound interest calculator with 3 years = 36 months[/URL], we get:
[B]1,686.18[/B]

You deposit $8500 in an account that pays 1.78% annual interest. Find the balance after 10 years whe

You deposit $8500 in an account that pays 1.78% annual interest. Find the balance after 10 years when the interest is compounded monthly.
10 years * 12 months per year = 120 months. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8500&nval=120&int=1.781&pl=Monthly']compound interest calculator[/URL], we get a balance of:
[B]$10,155.69[/B]

You have to pay 29 a month until you reach 850 how many months will that take

You have to pay 29 a month until you reach 850 how many months will that take.
Let m be the number of months. We set up the inequality:
29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=29m%3E%3D850&pl=Show+Interval+Notation']Type this inequality into our search engine[/URL], and we get:
m >= 29.31
We round up to the next integer month, to get [B]m = 30[/B].

You need $480 for a camp in 3 months. How much money do you need to save each week?

You need $480 for a camp in 3 months. How much money do you need to save each week?
[URL='https://www.mathcelebrity.com/timecon.php?quant=3&pl=Calculate&type=month']3 months[/URL] = 12 weeks
$480 / 12 weeks = [B]$40 per week[/B]

You open up a savings account. Your initial deposit is $300. You plan to add in $50 per month to sav

You open up a savings account. Your initial deposit is $300. You plan to add in $50 per month to save up for college. Write an equation to represent the situation.
Let m be the number of months. We have a Savings account function S(m):
S(m) = Monthly deposit * number of months + Initial Deposit
[B]S(m) = 50m + 300[/B]

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months.
Set up the cost function Y where x is the number of months you rent
[B]Y = 160x + 510[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/B]

Your grandfather gave you $12,000 a a graduation present. You decided to do the responsible thing an

Your grandfather gave you $12,000 a a graduation present. You decided to do the responsible thing and invest it. Your bank has a interest rate of 6.5%. How much money will you have after 10 years if the interest is compounded monthly?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=12000&nval=120&int=6.5&pl=Monthly']compound interest calculator[/URL], we have 10 years * 12 months = 120 months.
[B]$22,946.21[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]