$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 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]

$13 in the bank. You write a check for $17. What is your balance? When you write a check, it's a debit against your account, which means we subtract. So we start with $13. We subtract $17 Our balance is $13 - $17 = [B]-$4[/B]

$500 is deposited into a savings account. The bank offers a 3.5% interest rate and the money is left in the account for 5 years. How much interest is earned in this situation? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5000&nval=5&int=3.5&pl=Annually']compound interest calculator[/URL], we get interest earned as: [B]938.43[/B]

$800 is deposited in an account that pays 9% annual interest find balance after 4 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=800&nval=4&int=9&pl=Annually']compound interest calculator[/URL], we get: [B]1,129.27[/B]

$8000 are invested in a bank account at an interest rate of 10 percent per year. Find the amount in the bank after 5 years if interest is compounded annually Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8000&nval=5&int=10&pl=Annually']compound interest with balance calculator[/URL], we get: [B]12,884.08[/B]

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay? [U]Calculate Discount Percent:[/U] If the teachers got a 24% discount, that means they paid: 100% - 24% = 76% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent) [U]Calculate discount price:[/U] Discount Price = Full Price * (Discount Percent) Discount Price = 5230 * 0.76 Discount Price = 3974.80 Price per teacher = Discount Price / Number of Teachers Price per teacher = 3974.80 / 20 Price per teacher = [B]$198.74[/B]

2200 dollars is placed in an account with an annual interest rate of 7.25%. How much will be in the account after 29 years [URL='https://www.mathcelebrity.com/compoundint.php?bal=2200&nval=29&int=7.25&pl=Annually']Using our compound interest calculator[/URL], with an initial balance of 2,200, 29 years for time, and 7.25% annual interest rate, we get: [B]16,747.28[/B]

2900 dollars is placed in an account with an annual interest rate of 9%. Hoe much will be in the account after 13 years to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2900&nval=13&int=9&pl=Annually']compound interest with balance calculator[/URL], we get: [B]8,890.83[/B]

2900 dollars is placed in an account with annual interest rate of 9%. How much will be in the account after 13 years, round to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2090&nval=13&int=9&pl=Annually']compound interest calculato[/URL]r, we get a balance of: [B]6,407.53[/B]

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax Figure out the total cost before the discount: Total Cost before discount = Cases * Price per case Total Cost before discount = 3 cases * $21.95 per case Total Cost before discount = $65.85 Now, find the discounted value of the apples: Discounted Apple Price = Total Cost before discount * (1 - discount percent) Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2 Discounted ApplesPrice = $65.85 * 0.8 Discounted ApplesPrice = $52.68 Now, apply the sales tax to this discounted value to get the total bill: Total Bill = Discounted Apple Price * (1 + tax rate) Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075 Total Bill = $52.68 * 1.075 Total Bill = [B]$56.63[/B]

3 salads, 4 main dishes, and 2 desserts Total meal combinations are found by multiplying each salad, main dish, and dessert using the fundamental rule of counting. The fundamental rule of counting states, if there are a ways of doing one thing, b ways of doing another thing, and c ways of doing another thing, than the total combinations of all the ways are found by a * b * c. With 3 salads, 4 main dishes, and 2 desserts, our total meal combinations are: 3 * 4 * 2 = [B]24 different meal combinations.[/B]

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame. Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3. Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

5 shirts. 3 pants and 8 shoes how many outfits can you wear Using the fundamental rule of counting, we can have: 5 shirts * 3 pants * 8 shoes = [B]120 different outfits[/B]

6 numbers have a mean of 4. What is the total of the 6 numbers? Mean = Sum of numbers / Count of numbers Plug our Mean of 4 and our count of 6 into this equation: 4 = Sum/Total of Numbers / 6 Cross multiply: Sum/Total of Numbers = 6 * 4 Sum/Total of Numbers = [B]24[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/intbal.php?startbal=6700&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2024&pl=Annual+Credit']Using our balance with interest calculator[/URL], we get: [B]$42,485.94[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. show much will be in the account after 24 years, to the nearest cent ? Using our compound interest calculator, we get: [B]42,485.91 [MEDIA=youtube]0C25FB_4004[/MEDIA][/B]

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6700&nval=28&int=8.25&pl=Annually']balance with interest calculator[/URL], we get: 61,667.47

7 salads, 10 main dish, 6 dessert Using the Fundamental Rule of Counting, we have: 7 * 10 * 6 = 420 possible meals

7100 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the account after 30 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with compound interest calculator[/URL], we get: 66,646.40

7100 dollars is placed in an account with an interest of 7.75%. How much will be in the account after 30 years to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with interest calculator[/URL], we get: [B]$66,646.40[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the [URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=5.75&int=24&pl=Annually']Using our compound balance interest calculator[/URL], we get: [B]$26,525.61[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=24&int=5.75&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$29,459.12[/B]

7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the account after 11 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7900&nval=11&int=5.5&pl=Annually']compound interest calculator[/URL], we get: [B]14,236.53[/B]

8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 14 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=8300&nval=14&int=6.5&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$20,043.46[/B]

9000 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 17 years, to the nearest cent? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=9000&nval=17&int=8&pl=Annually']compound interest accumulated balance calculator[/URL], we get: [B]$33,300.16[/B]

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 $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given? Let the second discount be d. We're given: 480 * (1 - 0.3)(1 - d) = 285.60 480(0.7)(1 - d) = 285.60 336(1 - d) = 285.60 336 - 336d = 285.60 [URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get: d = [B]0.15 or 15%[/B]

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 helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how much will it cost after tax? [U]Calculate percent off first:[/U] 10% off means 90% off the price $18.50 * (1 - 0.1) $18.50 * (0.9) = 16.65 [U]Now, add 7% sales tax to the discounted price[/U] Price after sales tax = Discounted Price * 1.07 Price after sales tax = 16.65(1.07) [B]Price after sales tax = 17.82[/B]

A book is discounted 45%. If the original price is $40, what is the new price? 45% discount means we pay 100% - 45% = 55% 40 * 55% = [B]22[/B]

a book which was marked at $84 was sold for $75.60 .calculate the percent discount Using our [URL='https://www.mathcelebrity.com/markup.php?p1=84&m=&p2=+75.60&pl=Calculate']markdown calculator[/URL], we get: [B]10% markdown/percent discount[/B]

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this shelf take an additional 25% off." Leta picked out books from the discount shelf that had a regular price of $100. How much did Leta pay for the discounted books? 100 with 50% discount is $40 $50 with a 25% discount is $12.50 off $50 - $12.50 = [B]$37.50[/B]

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on the camera Using our [URL='https://www.mathcelebrity.com/markup.php?p1=450&m=&p2=+315&pl=Calculate']markdown calculator[/URL], we get: [B]-30%[/B]

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 certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.After how many hours will the bacteria count reach 10,000. Set up the doubling times: 0 | 8 1.5 | 16 3 | 32 4.5 | 64 6 | 128 7.5 | 256 9 | 512 10.5 | 1024 12 | 2048 13.5 | 4096 15 | 8192 16.5 | 16384 So at time [B]16.5[/B], we cross 10,000 bacteria.

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 clothing store buys shirts for [I]n[/I] dollars and then marks them up 50%. To reward their employees, the store gives a 50% discount to all employees. How much does an employee pay for a shirt? 50% = 0.5 Markup cost = (1 + 0.5)n Markup cost = 1.5n 50% discount: 1.5n/2 = [B]0.75n[/B]

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off of the discounted priced. How much does the coat cost now? Calculate discounted price: Discounted Price = Full Price * (1 - Discount Percentage) Discounted Price = 100 * (1 - 0.20) <-- Since 20% = 0.2 Discounted Price = 100 * (0.80) Discounted Price = 80 Now calculate marked down price off the discount price: Markdown Price = Discount Price * (1 - Markdown Percentage) Markdown Price = 80 * (1 - 0.30) <-- Since 30% = 0.3 Markdown Price = 80 * (0.70) Markdown Price = [B]56[/B]

A couple is opening a savings account for a newborn baby. They start with $3450 received in baby gifts. If no depositts or withdrawals are made, what is the balance of the account if it earns simple interest at 6% for 18 years? Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3450&int=6&t=18&pl=Simple+Interest']our simple interest calculator[/URL], we get: [B]7,176[/B]

A customer withdrew $100 from a bank account. The customer then deposited $33 the next day. Write and then evaluate an expression to show the net effect of these transactions. Withdrawals are negative since we take money away Deposits are positive since we add money So we have: [LIST] [*]100 withdrawal = -100 [*]33 deposit = +33 [/LIST] Our balance is: -100 + 33 = [B]-67 net[/B]

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold for $5.76 apiece. What is the mark-up, as a percentage? Using our [URL='https://www.mathcelebrity.com/markup.php?p1=3.80&m=&p2=5.76&pl=Calculate']markup calculator[/URL], we get: [B]51.58% markup[/B]

A family is taking a cross-country trip of 3000 miles by car. They are bringing two spare tires with them and want all six tires to go an equal distance. How many miles will each tire go? 3000 * 4 tires = 12,000 miles traveled 12,000 / 6 tires = [B]2,000 miles[/B]

A farmer sold 250 of his sheep, bought 35 and then bought 68. If he now has 190, how many did he begin with? Let's start his count with x. We have: x - 250 + 35 + 68 = 190 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-250%2B35%2B68%3D190&pl=Solve']equation solver[/URL], we get x = [B]337[/B]

A financial advisor has invested $7000 in two accounts. If one account contains x dollars, express the amount in the second account in terms of x The other account contains: [B]7000 - x[/B]

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print. We subtract 5 cm from the length and the width to account for the frame: Unframed Length: 80 - 5 = 75 Unframed Width: 65 - 5 = 60 Area of the unframed rectangle is: A = lw A = 75(60) A = [B]4,500 sq cm[/B]

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, and zinnias. if the gardener planted 47 plants, what kind of flower did he plant last? Let c be carnations, d be daffodils, l be larkspurs, t be tiger lillies, and z be zinnias. The order goes as follows: c, d, l, t, z. So each cycle of plants counts as 5 plants. We know that 9 * 5 = 45. So the gardener plants 9 full cycles. Which means they have 47 - 45 = 2 plans left over. In the order above, the second plant is the daffodil. So the gardener planted the [B]daffodil[/B] last. Now, can we shortcut this problem? Yes, using modulus. 47 plants, with 5 plants per cycle, we do [URL='https://www.mathcelebrity.com/modulus.php?num=47mod5&pl=Calculate+Modulus']47 mod 5 through our calculator[/URL], and get 2. So we have 2 plants left over, and the daffodil is the second plant.

A grandmother deposited $5,000 in an account that pays 8% per year compounded annually when her granddaughter was born. What will the value of the account be when the granddaughter reaches her 16th birthday? We have the accumulation function A(t) = 5,000(1.08)^t. For t = 16, we have: A(16) = 5,000(1.08)^16 A(16) = 5,000*3.42594264333 A(16) = [B]17,129.71[/B]

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost of the guitar including tax? Discount Amount = 0.2n Total paid after discount = n - 0.2n = 0.8n Tax amount: 0.8n * 0.08 = 0.064n After tax amount: 0.8n + 0.64n = [B]0.864n[/B]

a new savings account starts at $700 at a rate of 1.2% yearly. how much money will be in the account after 8 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=1.2&pl=Annually']balance and interest calculator with annual (yearly) compounding[/URL], we have: [B]770.09[/B]

A numerical pass code is required to open a car door. The pass code is five digits long and uses the digits 0-9. Numbers may be repeated in the pass code. How many different pass codes exist? 0-9 is 10 digits. Since digits can repeat, we use the fundamental rule of counting to get: 10 * 10 * 10 * 10 * 10 = [B]100,000 different pass codes[/B]

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the final cost [U]Calculate discounted price:[/U] Discounted price = Full price * (100% - discount percent) Discounted price = 129.99 * (100% - 20%) Discounted price = 129.99 * 80% Since 80% = 0.8, we have: Discounted price = 129.99 * 0.8 Discounted price = 103.99 [U]Calculate after tax cost:[/U] Tax Rate = Tax percent/100 Tax Rate = 8/100 Tax Rate = 0.08 After Tax cost = Discounted price * (1 + Tax rate) After Tax cost = 103.99 * (1 + 0.08) After Tax cost = 103.99 * 1.08 After Tax cost = [B]112.31[/B]

A pair of standard dice is rolled, how many possible outcomes are there? We want the number of outcomes in the sample space. The first die has 6 possibilities 1-6. The second die has 6 possibilities 1-6. Our sample space count is 6 x 6 = [B]36 different outcomes [/B] [LIST=1] [*](1, 1) [*](1, 2) [*](1, 3) [*](1, 4) [*](1, 5) [*](1, 6) [*](2, 1) [*](2, 2) [*](2, 3) [*](2, 4) [*](2, 5) [*](2, 6) [*](3, 1) [*](3, 2) [*](3, 3) [*](3, 4) [*](3, 5) [*](3, 6) [*](4, 1) [*](4, 2) [*](4, 3) [*](4, 4) [*](4, 5) [*](4, 6) [*](5, 1) [*](5, 2) [*](5, 3) [*](5, 4) [*](5, 5) [*](5, 6) [*](6, 1) [*](6, 2) [*](6, 3) [*](6, 4) [*](6, 5) [*](6, 6) [/LIST]

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this investment be worth in 10 years? If the interest was applied four times per year (known as quarterly compounding), calculate how much the investment would be worth after 10 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=10&int=4&pl=Annually']compound interest calculator[/URL], $500 @ 4% for 10 years is: $[B]740.12 [/B] Using [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=40&int=4&pl=Quarterly']quarterly compounding in our compound interest calculator[/URL], we have 10 years * 4 quarters per year = 40 periods, so we have: [B]$744.43[/B]

A person invests $9400 in an account at 5% interest compound annually. When will the value of the investment be $12,800. Let's take it one year at a time: Year 1: 9,400(1.05) = 9,870 Year 2: 9,870(1.05) = 10,363.50 Year 3: 10,363.50(1.05) = 10,881.68 Year 4: 10.881.68(1.05) = 11,425.76 Year 5: 11,425.76(1.05) = 11,997.05 Year 6: 11,997.05(1.05) = 12.596.90 Year 7: 12,596.90(1.05) = 13,226.74 So it take [B][U]7 years[/U][/B] to cross the $12,800 amount.

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get: V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get: V = 96,300 * e^(0.028 * 7) V = 96,300 * e^0.196 V = 96,300 * 1.21652690533 V = [B]$117,151.54[/B]

A project requires a $5000 investment. It pays out $1000 at year 1, $2000 at year 2, $3000 at year 3. The discount rate is 5%. Should you invest? Using our [URL='https://www.mathcelebrity.com/npv.php?matrix1=0%2C-5000%0D%0A1%2C1000%0D%0A2%2C2000%0D%0A3%2C3000&irr=5&pl=NPV']NPV calculator,[/URL] we get: NPV = 357.94. Because NPV > 0, we [B]should invest [MEDIA=youtube]jXvwCTDwQ1o[/MEDIA][/B]

A restaurant offers 20 appetizers and 40 main courses, how many ways can a person order a two course meal? Using the fundamental rule of counting, we can have: 20 appetizers * 40 main courses = [B]800 possible two-course meals[/B]

A restaurant offers the following options: [LIST] [*]Starter – soup or salad [*]Main – chicken, fish or vegetarian [*]Dessert – ice cream or cake [/LIST] How many possible different combinations of starter, main and dessert are there? Using the fundamental rule of counting, we have: 2 starters * 3 main courses * 2 desserts = [B]12 different combinations [MEDIA=youtube]-N9j7FQ8Le4[/MEDIA][/B]

A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500 Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7500&nval=8&int=15&pl=Annually']compound interest with balance calculator,[/URL] we get a balance of: [B]22,942.67[/B]

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale price be for water skis which regularly sell for $248? [U]Calculate Sale Price:[/U] Sale Price = Full Price * (1 - sale discount) Sale Price = 248 * (1 - 0.2) <-- since 20% is 0.2 Sale Price = 248 * (0.8) Sale Price = [B]198.40[/B]

A store is offering a 11% discount on all items. Write an equation relating the final price 11% discount means we pay 100% - 11% = 89% of the full price. Since 89% as a decimal is 0.89. With a final price f and an original price p, we have: [B]F = 0.89p[/B]

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an item to its list price L If we give a discount of 15%, then we pay 100% - 15% = 85% of the list price. 85% as a decimal is 0.85, So we have: L = 0.85S

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L. 18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price: S = L(1 - 0.18) [B]S = 0.82L[/B]

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales tax. How much will the toaster oven cost? [U]Calculate discounted price:[/U] Discounted Price = Full Price * (1 - Discount Percent) Since 30% = 0.3, we have Discounted Price = 35 * (1 - 0.3) Discounted Price = 35 * 0.7 Discounted Price = 24.5 Calculate after-tax amount: After-tax amount = Discounted Price * (1 + Tax Percent) Since 8% = 0.08, we have Discounted Price = 24.5 * (1 + 0.08) Discounted Price = 24.5 * 1.08 Discounted Price = [B]26.46[/B]

A three digit number, if the digits are unique [LIST=1] [*]For our first digit, we can start with anything but 0. So we have 9 options [*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options [*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options [/LIST] Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting: 9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax? Find the discounted price: 15% off of 192.94 Discounted Price = 192.94 * (1 - 0.15) <-- 15% as a decimal is 0.15, and 1 is 100%, so we subtract to get 85% of the original price Discounted Price =192.94(0.85) Discounted Price = $164 Now, add in the sales tax of 6% to the Discounted Price Price after sales tax = Discounted Price * 1.06 Price after sales tax = $164 * 1.06 [B]Price after sales tax = $173.84[/B]

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was $18,100, find the discount and the new price. Using our [URL='http://www.mathcelebrity.com/markup.php?p1=&m=+6&p2=++18100&pl=Calculate']discount calculator[/URL], we get: [B]Discount = $1,086 New Price = $17,014[/B]

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was 18,400, find the discount and the new price. First, find the discount amount: Discount Amount = 6% * 18,400 = [B]1,104 [/B] [U]Calculate discounted price:[/U] Discounted Price = Full Price - Discount Amount Discounted Price = 18,400 - 1,104 Discounted Price = 18,400 - 1,104 = [B]17,296[/B]

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Adam took money from his savings account to use as spending money on a trip to San Antonio. On Monday, he spent half his money. On Tuesday, he sp ent half of what was left. On Wednesday, he again spent half of his remaining money. On Thursday, he work up with very little money left, but again spent half of it. If Adam started the vacation with n dollars, how much money did he have at the end of Thursday? [LIST] [*]Start with: n [*]Monday: n * 1/2 = n/2 [*]Tuesday: n/2 * 1/2 = n/4 [*]Wednesday: n/4 * 1/2 = n/8 [*]Thursday: n/8 * 1/2 = [B]n/16[/B] [/LIST]

Alana puts $700.00 into an account to use for school expenses. The account earns 8% interest, compounded annually. How much will be in the account after 4 years? We use our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=4&pl=Annually']balance with interest calculator[/URL] and we get: [B]$958[/B]

Alice is making a sandwich to pack in her lunch. She has 2 different kinds of bread, 3 cheeses, 4 lunch meats, and 2 condiments to choose from. Assuming she uses one of each of bread, cheese, meat, and condiment, how many different sandwiches can she make? We use the Fundamental Rule of Counting [LIST] [*]Bread: 2 [*]Cheeses: 3 [*]Lunch Meats: 4 [*]Condiments: 2 [/LIST] 2 * 3 * 4 * 2 = [B]48 different sandwiches[/B]

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with? We start with a balance of b. Depositing 41 means we add to the account balance: b + 41 Writing checks for 31 and 13 means we subtract from the account balance: b + 41 - 31 - 13 The final balance is 81, so we set b + 41 - 31 - 13 equal to 81: b + 41 - 31 - 13 = 81 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get: b = [B]84[/B]

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]

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=4000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get an accumulated value of 4,960 Interest Paid = Accumulated Value - Principal Interest Paid = 4960 - 4000 Interest Paid = [B]960[/B]

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years? 365 days * 41 years + 10 leap year days = 14,975 days what is the lowest permutations count of n such that nP5 >= 14,975 W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone? Person A: x/2 job per hour Person B: 1/x job per hour Set up our equation: 1/x + 1/(2x) = 1/10 Multiply the first fraction by 2/2 to get common denominators; 2/(2x) + 1/(2x) = 1/10 Combine like terms 3/2x = 1/10 Cross multiply: 30 = 2x Divide each side by 2: [B]x = 15[/B]

An ice cream shop carries 6 ice cream flavors, 3 sauces, and 4 toppings. If a sundae has one scoop of ice cream, one sauce, and one topping, how many different sundaes can be created? Using the rule of counting, we have: We have 6 possible ice cream flavors * 3 possible sauces * 4 possible toppings = [B]72 possible sundaes[/B]

An initial deposit of $50 is now worth $400. The account earns 5.2% interest compounded continuously. Determine how long the money has been in the account. [URL='https://www.mathcelebrity.com/simpint.php?av=400&p=50&int=5.2&t=&pl=Continuous+Interest']Using our continuous interest compound calculator solving for t[/URL], we get: t =[B] 39.99 periods[/B]

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]

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years? Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get: [B]$5,128.15[/B]

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]

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Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/B]

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]

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blair’s bank account was overdrawn by $40. she spent $30 at the grocery store. what is the balance in her account now? The word [I]overdrawn[/I] means a negative balance. So we start with: -40 Spending 30 at the grocery store means we subtract 30 from our initial balance: -40 - 30 = [B]-70 or $70 overdrawn[/B]

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Bonnita deposited $4,500 into a savings account paying 3% interest compounded continuously. She plans on leaving the account alone for 7 years. How much money will she have at that time? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=3&t=7&pl=Continuous+Interest']compound interest calculator[/URL], we get: [B]$5551.55[/B]

Brad has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have in 3 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=40&nval=3&int=5&pl=Annually']Using our balance with interest calculator[/URL], we get [B]$46.31[/B].

Brenda invests $1535 in a savings account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 8 years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1535&int=3&t=8&pl=Continuous+Interest']continuous interest balance calculator[/URL], we get: [B]1,951.37 [MEDIA=youtube]vbYV6SYXtvs[/MEDIA][/B]

Bridget deposited $4500 at 6 percent simple interest. How much money was in the account at the end of three years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=6&t=3&pl=Simple+Interest']simple interest balance calculator[/URL], we get: $[B]5,310[/B]

camille has 7 blouses,2 skirts,3 pair of short pants and 5 pair of jeans.how many different outfits can he wear,assuming that he always wear a belt. Using the fundamental rule of counting, we find total amount of different outfits as follows: 7 blouses * 2 skirts * 3 pair of short pants * 5 pair of jeans = [B]210 outfits[/B].

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax Let the original price be p. p Apply 25% discount first, which is the same as subtracting 0.25: p(1 - 0.25) Subtract 30 for in store buck p(1 - 0.25) - 30 The phrase [I]no more than[/I] means an inequality using less than or equal to: p(1 - 0.25) - 30 <= 60 To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get: [B]p <= 120[/B]

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this. We have: 25f + 100c < 50 Note: We use < and not <= because it states less than in the problem.

Catherine has $400 in her checking account. She writes a check for $600. What is the balance in her account? Writing a check decreases the bank balance. So we have: $400 - $600 = [B]-$200[/B]

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Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this. We have [B]25f + 100c < 600[/B] as our inequality.

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Charlie has $2700 in his bank account. He spends $150 a week. How many weeks will have passed when Charlie has $600 in his bank account? Let w be the weeks that pass. We have the following equation for Charlie's balance: 2700 - 150w = 600 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=2700-150w%3D600&pl=Solve']type this equation into our math engine[/URL] and we get: w = [B]14[/B]

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two 4’s, you win $2; if you roll just one 4, you win $1 (and, in all of these cases you get your original $1 back). If you roll no 4’s, you lose your $1. Compute the expected payoff for chuck-a-luck. Expected payoff for each event = Event Probability * Event Payoff Expected payoff for 3 matches: 3(1/6 * 1/6 * 1/6) = 3/216 = 1/72 Expected payoff for 2 matches: 2(1/6 * 1/6 * 5/6) = 10/216 = 5/108 Expected payoff for 1 match: 1(1/6 * 5/6 * 5/6) = 25/216 Expected payoff for 0 matches: -1(5/6 * 5/6 * 5/6) = 125/216 Add all these up: (3 + 10 + 25 - 125)/216 -87/216 ~ [B]-0.40[/B]

Cody invests $4,734 in a retirement account with a fixed annual interest rate of 4% compounded continuously. What will the account balance be after 19 years? Using our c[URL='http://www.mathcelebrity.com/simpint.php?av=&p=4734&int=4&t=19&pl=Continuous+Interest']ontinuous interest compounding calculator[/URL], we get: [B]10,122.60[/B]

Coles paycheck was $257.20. He put 25% of it into his savings account and used 1/3 of what was left to pay bills. How much money does he have remaining from his paycheck? 25% is also 1/4. Calculate savings $257.20(0.25) = $64.3 We have 75% left over = $192.90 Coles pays 1/3 of this for bills = $192.90 * 1/3 = $64.30 Subtract the bills: $192.90 - $64.30 = [B]$128.60[/B]

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Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country. Set up our two given equations: [LIST=1] [*]A = 7B [*]A + B = 40,000,000 [/LIST] Substitute (1) into (2) (7B) + B = 40,000,000 Combine like terms 8B = 40,000,000 Divide each side by 8 [B]B = 5,000,000[/B] Substitute this into (1) A = 7(5,000,000) [B]A = 35,000,000[/B]

Customers arrive at the claims counter at the rate of 20 per hour (Poisson distributed). What is the probability that the arrival time between consecutive customers is less than five minutes? Use the [I]exponential distribution[/I] 20 per 60 minutes is 1 every 3 minutes 1/λ = 3 so λ = 0.333333333 Using the [URL='http://www.mathcelebrity.com/expodist.php?x=+5&l=0.333333333&pl=CDF']exponential distribution calculator[/URL], we get F(5,0.333333333) = [B]0.811124396848[/B]

Dale has a box that contains 20 American quarters and 20 Canadian quarters. If he takes them from the box one at a time, how many must he remove before he is guaranteed to have 5 quarters from the same country? Worst case scenario, Dale picks 4 American and 4 Canadian quarters which guarantees his next pick would be a 5th of either quarter. So the answer is 4 + 4 + 1 = [B]9[/B]

Dan bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 30 cards left. How many cards did Dan start with? Let the original collection count of cards be b. So we have (b + 8)/2 = 30 Cross multiply: b + 8 = 30 * 2 b + 8 = 60 [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B8%3D60&pl=Solve']Use the equation calculator[/URL] [B]b = 52 cards[/B]

Daniel invests £2200 into his bank account. He receives 10% per year simple interest. How much will Daniel have after 2 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=2200&int=10&t=2&pl=Simple+Interest']simple interest calculator[/URL], we get: [B]$2,640[/B]

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]

David has b dollars in his bank account; Claire has three times as much money as David. The sum of their money is $240. How much money does Claire have? David has b Claire has 3b since three times as much means we multiply b by 3 The sum of their money is found by adding David's bank balance to Claire's bank balance to get the equation: 3b + b = 240 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2Bb%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get: b = 60 So David has 60 dollars in his bank account. Therefore, Claire has: 3(60) = [B]180[/B]

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]

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12. Our givens are: [LIST] [*]I = 450 [*]P = 3000 [*]t = 3 [*]We want r [/LIST] 450 = 3000(r)(3) 450 = 9000r Divide each side by 9000 [B]r = 0.05[/B]

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after 10 years. Round your answer to the nearest penny if necessary. Annual compounding means we don't need to make adjustments to interest rate per compounding period. [URL='https://www.mathcelebrity.com/compoundint.php?bal=9538&nval=10&int=10&pl=Annually']Using our compound interest calculator[/URL], we get our new balance after 10 years of: [B]$24,739.12[/B]

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During your first year on the job, you deposit $2000 in an account that pays 8.5%, compounded continuously. What will be your balance after 35 years? [URL='https://www.mathcelebrity.com/simpint.php?av=&p=2000&int=8.5&t=35&pl=Continuous+Interest']Using our continuous compound balance calculator[/URL], we get a balance of [B]$39,179.25.[/B]

Dwayne wants to start a saving account at his local credit union. If he puts $8000 into a savings account with an annual interest rate of 1.1%, how much simple interest will he have earned after 6 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=1.1&t=6&pl=Simple+Interest']simple interest calculator[/URL], we get: $528 of interest earned.

Elijiah spent $6.20 for lunch everyday for 5 school days. He had $50 in his account. How much money was left over in his account? Elijiah starts with $50 He spends $6.20 per day * 5 days = 31 Leftover = 50 - 31 Leftover = [B]19[/B]

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take? Set up account equations A(d) where d is the number of days since time 0 for each account. Ethan A(d): 9079 + 19d Kurt A(d): 9259 + d The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other: 9079 + 19d = 9259 + d [URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B]. So in 10 days, both accounts will have equal amounts in them. Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation: A(10) = 9259 + 10 A(10) = $[B]9,269 [/B] After 10 days, both accounts have $9,269 in them.

Find the balance if $5000 is invested in an account paying 4.5% interest compounded continuously for 21 years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=5000&int=4.5&t=21&pl=Continuous+Interest']continuous compounding interest calculator[/URL], we get: [B]$12,864.07[/B]

Find the final amount of money in an account if $ 3,800 is deposited at 8% interest compounded annually and the money is left for 6 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3800&nval=6&int=8&pl=Annually']compound interest with balance calculator[/URL], we get: [B]$6,030.12[/B]

Consider the first 8 calculations of 7 to an exponent: [LIST] [*]7^1 = 7 [*]7^2 = 49 [*]7^3 = 343 [*]7^4 = 2,401 [*]7^5 = 16,807 [*]7^6 = 117,649 [*]7^7 = 823,543 [*]7^8 = 5,764,801 [/LIST] Take a look at the last digit of the first 8 calculations: 7, 9, 3, 1, 7, 9, 3, 1 The 7, 9, 3, 1 repeats through infinity. So every factor of 4, the cycle of 7, 9, 3, 1 restarts. Counting backwards from 2013, we know that 2012 is the largest number divisible by 4: 7^2013 = 7^2012 * 7^1 The cycle starts over after 2012. Which means the last digit of 7^2013 = [B]7 [MEDIA=youtube]Z157jj8R7Yc[/MEDIA][/B]

Following the birth of triplets, the grandparents deposit $30,000 in a college trust fund that earns 4.5% interest, compounded quarterly. How much will be in the account after 18 years? 18 years = 18 * 4 = 72 quarters. Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=30000&nval=72&int=4.5&pl=Quarterly']compound interest balance calculator[/URL], we have: [B]$67,132.95[/B]

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Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 18 years? [URL='https://www.mathcelebrity.com/simpint.php?av=&p=540&int=4.7&t=18&pl=Continuous+Interest']Using our compound interest balance calculator[/URL], we get: [B]$1,258.37[/B]

harley had $500 in his bank account at the beginning of the year. he spends $20 each week on food, clothing, and movie tickets. he wants to have more than $100 at the end of summer to make sure he has enough to purchase some new shoes before school starts. how many weeks, w, can harley withdraw money from his savings account and still have more than $100 to buy new shoes? Let the number of weeks be w. Harley needs $100 (or more) for shoes. We have the balance in Harley's account as: 500 - 20w >= 100 To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=500-20w%3E%3D100&pl=Solve']type it in our search engine[/URL] and we get: [B]w <= 20[/B]

How much money will there be in an account at the end of 10 years if $8000 is deposited at a 7.5% annual rate that is compounded continuously? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=8000&int=7.5&t=10&pl=Continuous+Interest']continuous compounding calculator[/URL], we get [B]$16,936[/B].

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 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]

Hunter puts $300.00 into an account to use for school expenses. The account earns 15% interest, compounded annually. How much will be in the account after 10 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=300&nval=10&int=15&pl=Annually']compound interest calculator[/URL], we get: [B]$1,213.67[/B]

If 5000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 9 years if interest is compounded annually. We assume the interest is compounded at the end of the year. Use the [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=9&i=10&check1=1&pl=Calculate']annuity immediate formula[/URL]: [B]67,897.39[/B]

If a person invests $360 In an account that pays 8% interests compounded annually, find the balance after 5 years [B]$528.95[/B] per our [URL='http://www.mathcelebrity.com/intbal.php?startbal=360&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2005&pl=Annual+Credit']balance calculator[/URL].

if joey has 5 swimsuits, 3 bicycles, and 4 pairs of running shoes, how many ways are there for joey to choose Using the Fundamental Rule of Counting, we have: 5 swimsuits * 3 bicycles * 4 pairs of running shoes = [B]60 possible choices[/B]

If the original price of an item was $30.00 and Joan only paid $24.00 for it, what percentage discount did Joan receive on her purchase? She received 6 dollars off of a 30 dollar purchase, so we have 6/30 = 1/5 = 0.2 = [B]20%[/B]

If you have $15,000 in an account with a 4.5% interest rate, compounded quarterly, how much money will you have in 25 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=15000&nval=100&int=4.5&pl=Quarterly']Using our compound interest calculator[/URL] with 25 years * 4 quarters per year = 100 periods of compounding, we get: [B]$45,913.96[/B]

if you own 5 pants, 8 shirts, and 3 jackets how many outfits can you make wearing 1 of each item? Using the Fundamental Rule of counting, we have: Total Pants * Total Shirts * Total Jackets 5 * 8 * 3 [B]120 [/B]

In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop? Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have the following equations: [LIST=1] [*]2b + 3t = 80 [*]b + t = 34 [/LIST] We can solve this set of simultaneous equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]b = 22[/B] [*][B]t = 12[/B] [/LIST]

In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have: b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already [/I] We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get: b = [B]6[/B]

In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee We don't want to count duplicates, so we have the following formula Tea Or Coffee = Tea + Coffee - Both Tea Or Coffee = 40 + 30 - 10 Tea Or Coffee = [B]60[/B]

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible? We want 8 choose 5, or 8C5. [URL='http://www.mathcelebrity.com/permutation.php?num=8&den=5&pl=Combinations']Typing this into the search engine[/URL] we get [B]56[/B].

In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]

Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12 a week. Write an equation to represent each girl. Let w equal the number of weeks, and f(w) be the amount of money in the account after w weeks: [LIST] [*]Ina: [B]f(w) = 40 + 8w[/B] [LIST] [*]We add because Ina saves money, so her account grows [/LIST] [*]Ree: [B]f(w) = 200 - 12w[/B] [LIST] [*]We subtract because Ree saves [/LIST] [/LIST]

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Jennifer added $120 to her savings account during July. If this brought her balance to $700, how much has she saved previously? We have a starting balance s. We're given: s + 120 = 700 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B120%3D700&pl=Solve']type it in our search engine[/URL] and we get: s = [B]580[/B]

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]

Jenny has $40 in her checking account. If she writes a check for $19 find her new account balance Writing a check means we take out of the account, so we subtract: Balance = $40 - $19 Balance = [B]$21[/B]

Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda has $260 in her savings account and adds $18 per week to the account. How long will it take Rhonda to have the same amount in her account as Jim? [U]Set up Jim's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 12w + 440 [U]Set up Rhonda's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 18w + 260 The problems asks for w where both savings functions equal each other: 12w + 440 = 18w + 260 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B440%3D18w%2B260&pl=Solve']type this equation into our math engine[/URL] and we get: w = [B]30[/B]

Jocelyn invested $3,700 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money would be in the account after 6 years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3700&int=1.5&t=6&pl=Continuous+Interest']continuous interest with balance calculator[/URL], we get: [B]$4,048.44[/B]

Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money? Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money. [U]Joe's Balance function B(w) where w is the number of weeks:[/U] 20 + 10w [U]Bria's Balance function B(w) where w is the number of weeks:[/U] 1000 - 15w [U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U] 20 + 10w = 1000 - 15w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get: w = 39.2 We round up to full week and get: w = [B]40[/B]

Joey puts $1,000.00 into an account to use for school expenses. The account earns 12% interest, compounded annually. How much will be in the account after 6 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1000&nval=6&int=12&pl=Annually']balance calculator[/URL], we get [B]$1,973.82[/B]

Joey withdrew $125 from his savings account. After the withdrawal, his balance was $785. How much was in his account initially? [U]Withdrawal means he took money out, which means his initial balance is found by adding back the withdrawal:[/U] Initial Balance = Current Balance + Withdrawal Initial Balance = 785 + 125 Initial Balance = [B]910[/B]

Joshua deposited $1200 into his two bank accounts. How much did he put in his savings account, which pays 9% per year in interest, and his chequing account, which pays 4% per year, if he earned $88 in interest after one year? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=1200&i1=9&i2=4&itot=88&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*][B]800 in savings[/B] [*][B]400 in checking[/B] [/LIST]

Julio had $20 in his account. He made two withdrawals of $15 and $25, and then he deposits $28. What is his account balance now? Note: Balances add and Withdrawals subtract. So we have: 20 - 15 - 25 + 28 [B]8[/B]

Karleys bank account was negative $12.14. she then deposited $21.63. What was her account balance negative 12.14 can be written as -12.14 She then deposited 21.63 which means we add 21.63 to her bank account balance: +21.63 Final account balance is: -12.14 + 21.63 = [B]$9.49[/B]

Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept form that represents the relationship between the amount in Kayla's bank account, A, and the number of weeks she has been spending, w [LIST] [*]Slope intercept form is written as A = mw + b [*]m = -150, since spending is a decrease [*]b = 1500, since this is what Kayla starts with when w = 0 [/LIST] [B]A = -150w + 1500[/B]

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account. Keith's balance is written as B(w) where w is the number of weeks passed since the beginning of summer. We have: B(w) = 500 - 25w The problem asks for B(w) = 200, so we set 500 - 25w = 200. [URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing 500 - 25w = 200 into the search engine[/URL], we get [B]w = 12[/B].

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account Our account balance is: 500 - 25w where w is the number of weeks. We want to know the following for w: 500 - 25w = 200 [URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 12[/B]

Kendra has $20 in a savings account. The interest rate is 10%, compounded annually. To the nearest cent, how much will she have in 2 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=20&nval=2&int=10&pl=Annually']balance with interest calculator[/URL], we get [B]$24.20[/B].

Kunio puts $2,200.00 into savings bonds that pay a simple interest rate of 2.4%. How much money will the bonds be worth at the end of 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=2200&int=2.4&t=4&pl=Simple+Interest']simple interest balance calculator[/URL], we his account will be worth [B]$2,411.20[/B] after 4 years

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]

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, Eric had $20,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $1880 in interest. How much did he invest in each account? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=20000&i1=10&i2=7&itot=1880&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1 = 16,000[/B] [*][B]Fund 2 = 4,000[/B] [/LIST]

Last year, Manuel had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account? The answer is $9,000 and $1,000 found on [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=7&i2=10&itot=730&pl=Calculate']this calculator[/URL].

Last year, Miguel had $10,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $800 in interest. How much did he invest in each account? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=5&i2=10&itot=800&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]4,000 in Fund 1 at 5%[/B] [*][B]6,000 in Fund 2 at 10%[/B] [/LIST]

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]

Levi invested $630 in an account paying an interest rate of 4.6% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $970? 3,425 days, per the [URL='http://www.mathcelebrity.com/compoundint.php?bal=630&nval=3425&int=4.6&pl=Daily']balance calculator[/URL].

License plate that is made up of 4 letters followed by 2 numbers Using the fundamental rule of counting, we have: 26 possible letters * 26 possible letters * 26 possible letters * 26 possible letters * 10 possible numbers * 10 possible numbers = [B]45,697,600 license plate combinations[/B]

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed We have 26 letters A-Z and 10 possible digits 0-9. Using the fundamental rule of counting, we have: 26 * 26 * 26 * 10 * 10 = [B]1,757,600 possible choices[/B]

License plates are made using 3 letters followed by 3 digits. How many plates can be made of repetition of letters and digits is allowed We have 26 letters in the alphabet We have 10 digits [0-9] The problem asks for the following license plate scenario of Letters (L) and Digits (D) LLLDDD The number of plates we can make using L = 26 and D = 10 using the fundamental rule of counting is: Number of License Plates = 26 * 26 * 26 * 10 * 10 * 10 Number of License Plates = [B]17,576,000[/B]

Lisa has 5 skirts, 10 blouses, and 4 jackets. How many 3-piece outfits can she put together assuming any piece goes with any other? Using the fundamental rule of counting, we have: 5 * 10 * 4 = [B]200 different 3-piece outfits[/B]

Lisa wants to rent a boat and spend less than $52. The boat costs $7 per hour, and Lisa has a discount coupon for $4 off. What are the possible numbers of hours Lisa could rent the boat? Calculate discounted cost: Discounted cost = Full Cost - Coupon Discounted cost = 52 - 7 Discounted cost = 45 Since price equals rate * hours (h), and we want the inequality (less than) we have: 7h < 52 Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7h%3C52&pl=Show+Interval+Notation']inequality calculator,[/URL] we see that: [B]h < 7.42[/B]

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent? This is an annuity due, since the first payment is made on the date of purchase. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many nickels and dimes does Lucas have? 1 + 3 + 2 = 6. Quarters account for 2/6 which is 1/3 of the total coin count. Let x be the total number of coins. We have: 1/3x = 10 Multiply each side by 3 x = 30 We have the following ratios and totals: [LIST] [*]Nickels: 1/6 * 30 = [B]5 nickels[/B] [*]Dimes: 3/6 * 30 = [B]15 dimes[/B] [*]Quarters: 2/6 * 30 = [B]10 quarters[/B] [/LIST]

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one? Let the total bill be b. We have: 0.15b > 21 <-- Since 15% is 0.15 Using our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=0.15b%3E21&pl=Show+Interval+Notation']inequality calculator[/URL], we get [B]b>140[/B]. So any bill greater than $140 will make the 15% off option the best one, since the discount will be higher than $21.

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]

Mary paid 1.97 for toothpaste and a bar of soap using a discount coupon if the toothpaste cost 1.29 and the song cost 83 cents. What is the value of the discount coupon? Find the full price package: 1.29 + 0.83 = 2.12 The value of the discount coupon is the money off, so: 2.12 - 1.97 = [B]0.15[/B]

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 has $3,000 in a savings account that earns 10% interest per year. How much will he have in 3 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=10&pl=Annually']compound interest with balance calculator[/URL], we get: [B]$3,993[/B]

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Miguel has $80 in his bank and saves $2 a week. Jesse has $30 in his bank but saves $7 a week. In how many weeks will Jesse have more in his bank than Miguel? [U]Set up the Bank value B(w) for Miguel where w is the number of weeks[/U] B(w) = Savings Per week * w + Current Bank Balance B(w) = 2w + 80 [U]Set up the Bank value B(w) for Jesse where w is the number of weeks[/U] B(w) = Savings Per week * w + Current Bank Balance B(w) = 7w + 30 The problem asks when Jesse's account will be more than Miguel's. So we set up an inequality where: 7w + 30 > 2w + 80 To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B30%3E2w%2B80&pl=Solve']type it in our search engine[/URL] and we get: [B]w > 10[/B]

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Mr. Crews goes to Publix and spends $81.25 on groceries. He pays the cashier with a hundred dollar bill. How much change will Mr. Crews get back from the cashier? Using our [URL='https://www.mathcelebrity.com/changecounter.php?cash=100&bill=81.25&pl=Calculate+Change+Amount']change calculator[/URL], we get: [B]$18.75[/B]

Ms. Gonzales is investing $17000 at an annual interest rate of 6% compounded continuously. How much money will be in the account after 16 years? Round your answer to the nearest hundredth (two decimal places). Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=17000&int=6&t=16&pl=Continuous+Interest']continuous interest calculator[/URL], we get: [B]44,398.84[/B]

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Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I] [I][/I] Set up the Account equation A(w) where w is the number of weeks that pass. Nancy (we add since savings means she accumulates [B]more[/B]): A(w) = 25w + 435 Shane (we subtract since spending means he loses [B]more[/B]): A(w) = 875 - 15w Set both A(w) equations equal to each other to since we want to see what w is when the account are equal: 25w + 435 = 875 - 15w [URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get: w =[B] 11[/B]

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Nick opens a bank account with $50. Each week after, he deposits $15. In how many weeks will he have saved $500 Start with remaining balance: 500 - 50 = 450 Now figure out how many weeks, at 15 per week, to get 450 450/15 = [B]30 weeks[/B]

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Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent. [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get: A = [B]1,521.96[/B]

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]

On the day of a child's birth, a deposit of $25,000 is made in a trust fund that pays 8.5% interest. Determine that balance in this account on the child's 25th birthday. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=25&int=8.5&pl=Annually']compound interest calculator[/URL], we get: [B]192,169.06 [/B]

Patricia has $425.82 in her checking account. How much does she have in her account after she makes a deposit of $120.75 and a withdrawal of $185.90? Start with $425.82 Deposits mean we [B]add[/B] money to the bank account: 425.82 + 120.75 = 546.57 Our new balance is 546.57. Withdrawals mean we [B]subtract[/B] money from the bank account: 546.57 - 185.90 = [B]360.67[/B]

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.

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Rachel deposits $6000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=6000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get interest paid of [B]$1,440[/B]

Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount? Let Rachel's account value R(w) where w is the number of weeks be: R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance. Let Roy's account value R(w) where w is the number of weeks be: R(w) = 15w Set them equal to each other: 200 - 25w = 15w To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=200-25w%3D15w&pl=Solve']we type it into our search engine[/URL] and get: [B]w = 5[/B]

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years? The formula for [U]interest[/U] using simple interest is: I = Prt where P = Principal, r = interest, and t = time. We're given P = 500, r =0.04, and t = 4. So we plug this in and get: I = 500(0.04)(4) I = [B]80[/B]

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Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit? Simple interest formula: A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest. Plugging in our numbers, we get: 400 = P(1 + 0.08(8)) 400 = P(1 + 0.64) 400 = 1.64P 1.64P = 400 [URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get: P = [B]$243.90[/B]

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random. a. What is the probability that you choose a red or even numbered ball? b. What is the probability you choose a green ball or a ball numbered less than 5? a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Red and Even balls are {2, 4, 6, 8, 10, 12} Our probability is: P(Red or Even) = P(Red) + P(Even) - P(Red and Even) P(Red or Even) = 13/18 + 9/18 - 6/18 P(Red or Even) = 16/18 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have: P(Red or Even) = [B]16/18[/B] [B][/B] b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count: We have 18 total balls, so this is our denonminator for our fractions. Green and less than 5 does not exist, so we have no intersection Our probability is: P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5) P(Green or Less Than 5) = 5/18 + 4/18 - 0 P(Green or Less Than 5) = 9/18 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have: P(Red or Even) = [B]1/2[/B]

Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal? Each week, Sara's account value is: 800 - 20w <-- Subtract because Sara withdraws money each week Each week, Jordan's account value is: 500 + 30w <-- Add because Jordan deposits money each week Set them equal to each other: 800 - 20w = 500 + 30w Using our [URL='http://www.mathcelebrity.com/1unk.php?num=800-20w%3D500%2B30w&pl=Solve']equation solver[/URL], we get w = 6. Check our work: 800 - 20(6) 800 - 120 680 500 + 30(6) 500 + 180 680

Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left? Let w be the number of weeks. We have the following equation for the Balance after w weeks: B(w) = 250 - 25w [I]we subtract for withdrawals[/I] The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below: 250 - 25w >= 0 To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get: w <= [B]10 So Sarah can withdrawal for up to 10 weeks[/B]

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces. Let x be the number of hours Sarah baby sits. Then her account value y is: y = [B]30x + 300[/B]

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Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each has 10 numbers 0-9). If Seth can try one lock combination per second, how many seconds will it take him to try every possible lock combination? Start with 0001, 0002, all the way to 9999 [URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=0&num2=9999&pl=Count']When you do this[/URL], you get 10,000 combinations. One per second = 10,000 seconds

Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every student in her math class. She only has 5 remaining. How many students are in her class? Let the number of students be s. We have a situation described by the following equation: 4s + 5 = 97 <-- We add 5 since it's left over to get to 97 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D97&pl=Solve']We type this equation into the search engine[/URL] and we get: s = [B]23[/B]

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza? [U]Determine additional amount the pizzas would have cost without the coupon[/U] 6 pizzas * 3 per pizza = 18 [U]Add 18 to our discount price of 38.94[/U] Full price for 6 large pizzas = 38.94 + 18 Full price for 6 large pizzas = 56.94 Let x = full price per pizza before the discount. Set up our equation: 6x = 56.94 Divide each side by 6 [B]x = $9.49[/B]

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Steve had $200 in his bank account. He made a deposit of $75 and then made a withdrawal of $90. How much money does Steve have in his account now? We add deposits 200 + 75 = 275 We subtract withdrawals 275 - 90 = [B]185[/B]

Steve Has Overdrawn His Checking Account By $27. His Bank Charged Him $15 For An Overdraft Fee Then He Quickly Deposited $100. What Is His Current Balance? [LIST=1] [*]Overdrawn means money he doesn't have, so we go into the negative. Start with -27. [*]A bank charge of $15 means he goes in the negative another $15, so -27 - 15 = -42 [*]Then he deposits $100, so his balance is: $100 - 42 = [B]$58[/B] [/LIST]

Suppose $10000 is invested in a savings account paying 8% interest per year , after 5 years how much would be in the account compounded continuously Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=10000&int=8&t=5&pl=Continuous+Interest']continuous compounding calculator[/URL], we get 14,918.25

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%? [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=50&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']50% proportion probability[/URL]: z = 2.04124145232 [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+35&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']35% proportion probability[/URL]: z = -1.02062072616 Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28-1.02062072616

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]

Suppose you deposit $3000 in an account paying 2% annual interest, compounded continuously. Use A=Pert to find the balance after 5 years. A = $3,000 * e^0.02(5) A = $3,000 * e^0.1 A = $3,000 * 1.105171 A = [B]$3,315.51[/B]

Suppose you deposited $1200 in an account paying a compound interest rate of 6.25% quarterly, what would the account balance be after 10 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=1200&nval=40&int=6.25&pl=Quarterly']Using our compound interest with balance calculator[/URL], we get: [B]$2,231.09[/B]

Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same? Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance [LIST] [*]You --> B(w) = 18.25w + 28 [*]Your friend --> B(w) = 161 - 15w [/LIST] Set them equal to each other 18.25w + 28 = 161 - 15w [URL='http://www.mathcelebrity.com/1unk.php?num=18.25w%2B28%3D161-15w&pl=Solve']Type that problem into the search engine[/URL], and you get [B]w = 4[/B].

Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1600&int=4.6&t=4&pl=Continuous+Interest']continuous compound calculator[/URL], we get $1,923.23

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The average of 171 and x? The phrase [I]average[/I] means add up all the items in the number set, divided by the count of items in the number set. Our number set in this case is {171, x} which has 2 elements. Therefore, our average is: [B](171 + x)/2[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers? The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers. Calculate the sum of the first group of numbers S1: Average = S1 / n1 18 = S1 / 20 S1 = 20 * 18 S1 =360 Calculate the sum of the second group of numbers S2: Average = S2 / n2 20 = S2 / 18 S2 = 18 * 20 S2 =360 Our average of averages is found by the following: A = (S1 + S2)/(n1 + n2) A = (360 + 360)/(20 + 18) A = 720/38 [B]A = 18.947[/B]

the average of two numbers x and y Average is the sum divided by the count: Sum: x + y We have 2 numbers, so we divide (x + y) by 2 [B](x + y)/2[/B]

the balance of an account after $40 withdrawal Let the balance be b. A withdrawal means a [U]reduction[/U][I] in the balance[/I]. So we have [B]b - 40[/B]

the initial deposit in a bank account was $6000 and it has an annual interest rate of 4.5%. Find the amount of money in the bank after 3 years Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6000&nval=4.5&int=3&pl=Annually']balance and interest calculator[/URL], we get: [B]$6,853.60[/B]

the mean of 12 scores is 8.8 . what is the sum of the scores ? The Mean is denoted as: Mean = Sum / count We're given: 8.8 = Sum / 12 Cross multiply and we get: Sum = 8.8*12 Sum = [B]105.6[/B]

The original price of a computer was $895.00. Eleanor had a 25% off coupon which she was able to use to make the purchase. If sales tax of 6.5% was added after the discount was taken, how much did Eleanor pay altogether for the computer? First, apply the discount: $895 * 25% = $223.75 $895 - $223.75 = $671.25 Now, apply sales tax of 6.5% to this discount price of $671.25 $671.25 * 1.065 = [B]$714.88[/B]

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 population of a town is currently 22,000. This represents an increase of 40% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole number if necessary. To get the population 5 years ago, we'd discount the current population of 22,000 by 40%. We can write a 40% discount as 1.4. Population 5 years ago = 22,000/1.4 Population 5 years ago = 15,714.29 Rounding to the nearest whole number, we get [B]15,714[/B]

The regular price for a television is Q dollars. Each Saturday televisions are 20% off (The discount is .2Q). What is the price of a television on Saturday in terms of Q? Q = Regular Price .2Q = Discount Discounted Price = Q - .2Q = [B]0.8Q[/B]

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the shirt has been discounted? Using our [URL='http://www.mathcelebrity.com/markup.php?p1=19&m=&p2=++13.30&pl=Calculate']markdown calculator[/URL], we get a 30% markdown, or sale.

The sale price of an item that is discounted by 20% of its list price L S = L - 20%/100 * L S = L - 0.20L [B]S = 0.8L[/B]

The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase? If Kyle bought the player, he has 243 - 210 = 33 left over. Each cd is 11, so set up an equation to see how many CDs he bought: 11x = 33 Divide each side by 11 [B]x = 3[/B]

The school council began the year with a $600 credit to their account, but they spent $2,000 on new books for classrooms. How much must the PTA earn through fundraising to break even? +600 - 2000 = -1,400. Break even means no profit or loss. So the PTA must earn [B]1,400 [/B]to break even on the -1,400

the sum of 3 consecutive natural numbers, the first of which is n Natural numbers are counting numbers, so we the following expression: n + (n + 1) + (n + 2) Combine n terms and constants: (n + n + n) + (1 + 2) [B]3n + 3 Also expressed as 3(n + 1)[/B]

Theodore invests $17,000 at 9% simple interest for 1 year. How much is in the account at the end of the 1 year period. Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=17000&int=9&t=1&pl=Simple+Interest']balance calculator with simple interest[/URL], we have: [B]18,530[/B]

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44? We want 45, 46, … 113 The formula to get inclusive number count between and including 2 numbers is: Total numbers = L - S + 1 Total numbers = 113 - 45 + 1 Total numbers = 69 That is 69 possible numbers. We draw this out of a total of 113 [B]P(Number > 44) = 69/113 [B]P(Number > 44) [/B]= 0.610619 [MEDIA=youtube]BLBVcpdHqXU[/MEDIA][/B]

There are some red counters and some yellow counters in the ratio 1:5. There are 20 yellow counters in the bag. Set up a proportion where x is the amount of red counters to 20 yellow counters 1/5 = x/20 Enter that in the search engine and our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=x&den1=5&den2=20&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] gives us: [B]x = 4[/B]

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue? Find the total number of marbles in the bag: Total marbles = 5 blue + 6 red + 2 green Total marbles = 13 The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows: Blue, Not Blue Not Blue, Blue The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time. The probability of not drawing a blue is (6 + 2)/13 = 8/13 And since each of the 2 draws are independent of each other, we multiply the probability of each draw: Blue, Not Blue = 5/13 * 8/13 =40/169 Not Blue, Blue = 8/13 * 5/13 = 40/169 We add both probabilities since they both count under our scenario: 40/169 + 40/169 = 80/169 Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore. So our probability stated in terms of a fraction is 80/169 [URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&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']Stated in terms of a decimal[/URL], it's 0.4734

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year. [B][U]Figure out the linear change from 2010 to 2020[/U][/B] Number of years = 2020 - 2010 Number of years = 10 [B][U]Figure out the number of graphic designer job increases:[/U][/B] Number of graphic designer job increases = 312,500 - 286,200 Number of graphic designer job increases = 26,300 [B][U]Figure out the number of graphic designer jobs added per year[/U][/B] Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years Graphic designer jobs added per year = 26,300 / 10 Graphic designer jobs added per year = 2,630 [U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U] G(y) = 286,200 + 2,630(y - 2010) [B][U]Multiply through and simplify:[/U][/B] G(y) = 286,200 + 2,630(y - 2010) G(y) = 286,200 + 2,630y - 5,286,300 [B]G(y) = 2,630y - 5,000,100[/B]

Three people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25. The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip. When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go? [B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27 What we have is the cost ($27) plus the refund ($3) = $30. The $30 that was originally paid is accounted for as follows: Restaurant + regular waitress tip: $25 Three people: $3 (refund) Waitress: $2 (extra tip) $25 + $3 + $2 = $30[/B]

To make an international telephone call, you need the code for the country you are calling. The code for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country. If they are three consecutive integers, then we have: [LIST=1] [*]B = A + 1 [*]C = B + 1, which means C = A + 2 [*]A + B + C = 90 [/LIST] Substitute (1) and (2) into (3) A + (A + 1) + (A + 2) = 90 Combine like terms 3A + 3 = 90 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3a%2B3%3D90&pl=Solve']equation calculator[/URL], we get: [B]A = 29[/B] Which means: [LIST] [*]B = A + 1 [*]B = 29 + 1 [*][B]B = 30[/B] [*]C = A + 2 [*]C = 29 + 2 [*][B]C = 31[/B] [/LIST] So we have [B](A, B, C) = (29, 30, 31)[/B]

Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food a.) write an equation that relates the amount in the account (a) with the number of (w) weeks b.) How many weeks will it take until Tyler runs out of money? [U]Part a) where w is the number of weeks[/U] a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I] a = [B]1200 - 21w [/B] [U]Part b)[/U] We want to know the number of weeks it takes where a = 0. So we have: 1200 - 21w = 0 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-21w%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: w = 57.14 weeks The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]

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Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat? A few things to build this problem: [LIST=1] [*]Discount subtracts from our total [*]Cost = Hourly rate * hours [*]Less than means an inequality using the < sign [/LIST] Our inequality is: 8h - 7 < 41 To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get: h < [B]6[/B]

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60% are of working age. Within that working-age group, women account for 53%. Of the working-age females, 42% of them are employed in farming. What is the total number of potential customers for your fertilizer? [U]Our sample population is found by this product:[/U] Female farmers of working age in Ghana = Total people in Ghana *[I] Working Age[/I] * Women of working Age * Farmers Since 60% = 0.6, 53% = 0.53, and 42% = 0.42, we have Female farmers of working age in Ghana = 22,600,000 * 0.6 * 0.53 * 0.42 Female farmers of working age in Ghana = [B]3,018,456[/B]

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 $150 into an account that yields 2% interest compounded quarterly. How much money will you have after 5 years? 2% per year compounded quarterly equals 2/4 = 0.5% per quarter. 5 years * 4 quarter per year = 20 quarters of compounding. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=150&nval=20&int=2&pl=Quarterly']balance calculator[/URL], we get [B]$165.73[/B] in the account after 20 years.

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 $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest? The simple interest formula for the accumulated balance is: Prt = I We are given P = 2,000, r = 0.04, and I = 500. 2000(0.04)t = 500 80t = 500 Divide each side by 80 t = [B]6.25 years [MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]

you deposit $2000 in an account that pays 3% annual interest. Find the balance after 10 years if the interest is compounded quarterly. Please give your answer to 2 decimal places. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2000&nval=40&int=3&pl=Quarterly']compound interest calculator, with 10 * 4 = 40 quarters[/URL], we have: [B]$2,696.70[/B]

You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years. The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is: A = B(1 + i)^n [U]Givens[/U] [LIST] [*]4 years of quarters = 4 * 4 = 16 quarters. So this is t. [*]Interest per quarter = 5/4 = 1.25% [*]Initial Balance (B) = 750. [/LIST] Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A: [B]$914.92[/B]

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 $110 saved in your bank account. You want to save $15 every week. Let x be the amount of weeks and y be the total amount saved. Savings mean we add to the bank balance, so we have: [B]y = 15x + 110[/B]

You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance? [U]Set up the savings account S(w) for you where w is the number of weeks[/U] S(w) = 140 + 10w [U]Set up the savings account S(w) for your friend where w is the number of weeks[/U] S(w) = 95 + 19w The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other: 140 + 10w = 95 + 19w To solve this equation for w, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2B10w%3D95%2B19w&pl=Solve']we type it in the search engine[/URL] and get: w = [B]5[/B]

You have $16 and a coupon for a $5 discount at a local supermarket. A bottle of olive oil costs $7. How many bottles of olive oil can you buy? A $5 discount gives you $16 + $5 = $21 of buying power. With olive oil at $7 per bottle, we have $21/$7 = [B]3 bottles of olive oil[/B] you can purchase

You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund Fund A and Fund B to produce an annual interest income of $14,750? You should invest $______in Fund A and $___________in Fund B. Equation is x(.079) + (250,000 - x).054 = 14,750 .025x + 13,500 = 14,750 .025x = 1,250 [B]x = 50,000 for Fund A[/B] So at 5.4%, we have 250,000 - 50,000 = [B]200,000[/B] for the other fund B.

You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=1300&nval=10&int=5&pl=Annually']compound interest balance calculator[/URL], we get: [B]$2,117.56[/B]

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 split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain. Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation: 05a + (1500 - a).04 = 69.50 Simplifying, we get: 0.05a + 1560 - 0.04a = 69.50 0.01a + 60 = 69.50 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.01a%2B60%3D69.50&pl=Solve']equation solver[/URL], we get: [B]a = 950[/B] So this means Account B is b = 1500 - 950 = [B]550[/B]

you start with 150$ in year bank account if you save $28 a year with equation would model your savings find equation. We create a savings function S(y) where y is the number of years since the start. S(y) = Savings per year * y + initial savings [B]S(y) = 28y + 150[/B]

Your friend deposits 9500$ in an investment account that earns 2.1% annual interest find the balance after 11 years when the interest is compounded quarterly 11 years * 4 quarters per year = 44 quarters Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=9500&nval=44&int=2.1&pl=Quarterly']compound interest with balance calculator[/URL], we have: [B]11,961.43[/B]

Zachary has 25 country music CDs, which are one-fifth of his CD collection. How many CDs does Zachary have? Let the number of Zachary's CD's be: 25 * 1/5 = 5 country music CD's

Zoey invested $230 in an account paying an interest rate of 6.3% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 12 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=230&nval=4380&int=6.3&pl=Daily']compound interest calculator with 12*365 = 4380 for days,[/URL] we have a balance of: [B]$489.81[/B]