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 If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?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 car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. Set up the depreciation equation D(t) where t is the number of years in the life of the car: D(t) = 24,000 * (1 - 0.3)^t D(t) = 24000 * (0.7)^t The problem asks for D(t)<=7300 24000 * (0.7)^t = 7300 Divide each side by 24000 (0.7)^t = 7300/24000 (0.7)^t= 0.30416666666 Take the natural log of both sides: LN(0.7^t) = -1.190179482215518 Using the natural log identities, we have: t * LN(0.7) = -1.190179482215518 t * -0.35667494393873245= -1.190179482215518 Divide each side by -0.35667494393873245 t = 3.33687437943 [B]Rounding this up, we have t = 4[/B]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium? Let the number of fish be f. We have the following inequality where "at most" means less than or equal to: 3.19f <= 35 [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get: f <= 10.917 Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . What will the population be after 12 years? Use the calculator provided and round your answer to the nearest whole number. Using our [URL='http://www.mathcelebrity.com/population-growth-calculator.php?num=acityhasapopulationof260000people.supposethateachyearthepopulationgrowsby8.75%.whatwillthepopulationbeafter12years?usethecalculatorprovidedandroundyouranswertothenearestwholenumber&pl=Calculate']population growth calculator,[/URL] we get P = [B]711,417[/B]

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number. We build the following exponential equation: Final Balance = Initial Balance * (1 + growth rate)^time Final Balance = 3100(1.04)^6 Final Balance = 3100 * 1.2653190185 Final Balance = 3922.48895734 The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U] Final Balance = [B]3,922[/B]

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer generates a multiple of 5 [URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']Multiples of 5[/URL]: {1, 5, 25} So we have the probability of a random number multiple of 5 is [B]3/25[/B]

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

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number. 44.9 quarts * 32 fluid ounce / quart = 1,436.8 if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get: [B]1,437 fluid ounces[/B]

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

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1. Set up the price function P(x) [B]P(x) = 0.43 + 0.29(x - 1)[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number. P(green) = Total Green / Total spaces P(green) = 2/6 We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get: P(green) = [B]1/3[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel? Set up the cost function C(m) where m is the number of miles: C(m) = 0.65m + 1.75 If Erica has $10, then C(m) = 10, so we have: 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get m = 12.69 if the answer asks for whole number, then we round down to m = 12

A third of a pizza is 400 calories. How many calories in the whole pizza? Let c be the number of calories in the whole pizza. WE have: c/3 = 400 To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=c&num2=400&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and get: c = [B]1,200[/B]

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number? We calculate the population of the town as P(t) where t is the time in years since now. P(t) = 12000(1.05)^t The problem asks for P(12) P(12) = 12000(1.05)^12 P(12) = 12000(1.79585632602) P(12) = [B]21550[/B] <- nearest whole number

Add all the whole numbers 1 through 100 [URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=1&num2=100&pl=Sum']Using our inclusive number word problem calculator[/URL], we get: 5,050

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What is the maximum number of concrete blocks that the elevator can lift? Total blocks liftable = Lift Max / Weight per block Total blocks liftable = 4400 / 41 Total blocks liftable = 107.31 We round down to whole blocks and we get [B]107[/B]

are all integers whole numbers true or false [B]False [/B] [LIST] [*]All whole numbers are integers but not all integers are whole numbers. [*]Whole numbers are positive integers. Which means negative integers are not whole numbers [*]-1 for instance is an integer, but not a whole number [/LIST]

Charlene wants to invest $10,000 long enough for it to grow to at least $20,000. The compound interest rate is 6% p.a. How many whole number of years does she need to invest the money for so that it grows to her $20,000 target? We want 10,000(1.06)^n = 20,000. But what the problem asks for is how long it will take money to double. We can use a shortcut called the Rule of 72. [URL='https://www.mathcelebrity.com/rule72.php?num=6&pl=Calculate']Using the Rule of 72 at 6%[/URL], we get [B]12 years[/B].

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Gino has 7 whole pineapples. He cuts each whole into 4 equal parts. Write an improper fraction for the cut parts of pineapples. Take our whole pineapples divided by the number of equal parts: [B]7/4[/B]

How many 8$, tickets can I get for 100$ Tickets = Total Money / price per ticket Tickets = 100/8 Tickets = [B]12.5 [/B] If the problem asks for a whole number, this means you cannot have a partial ticket. Therefore, we round down to [B]12 tickets[/B]

It costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many games can he Bowl? Let g be the number of games. The cost for Wayne is: C(g) = Cost per game * number of games + shoe rental 4.25g + 1.90 = C(g) We're given C(g) = 20, so we have: 4.25g + 1.90 = 20 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=4.25g%2B1.90%3D20&pl=Solve']equation solver[/URL] for g, we get: g = 4.25 We need whole games, we we round down to [B]4 games[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number. Calculate earnings per lifespan: Earnings per lifespan = lifespan in years * Annual Earnings Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year) Earnings per lifespan = 8,085,480 Calculate the number of lifespans needed to match Jeff Bezos earnings: Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan Number of lifespans = 143,100,000,000 / 8,085,480 Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s + 57 = 105 We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get: s = [B]3.2 or 3 whole shirts[/B]

Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each. Let the number of t-shirts be t. Lisa can spend up to, but not more than 150. We have the following inequality: 14t + 58 <= 150 To solve this inequality, we [URL='https://www.mathcelebrity.com/1unk.php?num=14j%2B58%3C%3D150&pl=Solve']type it in our search engine[/URL] and we get: t <= 6.57 To round to a whole number, we round down to [B]t = 6 [/B]

Nancy shot a 16 on 4 holes of golf. At this rate, what can she expect her score to be if she plays 18 holes? Round to the nearest whole number Set up a proportion of score to holes of golf where s is the score for 18 holes: 16/4 = s/18 To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=s&den1=4&den2=18&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: s = [B]72[/B]

Notebooks cost $1.39 each. What are the possible numbers of notebooks that can be purchased with $10? Let n be the number of notebooks you can purchase. We have the following inequality: 1.39n <= 10 Divide each side by 1.39 n <= 7.194 We want whole notebooks, we cannot buy fractions of notebooks, so we have: n <= 7 The question asks for the possible numbers of notebooks we can buy. This implies we buy at least 1, but our inequality says not more than 7. So our number set is: [B]N = {1, 2, 3, 4, 5, 6, 7}[/B]

Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number. We have the equation y(x): y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97 The problem asks for y(2020). So x = 2020 - 2010 = 10. y(10) = 25,000(0.97)^10 y(10) = 25,000(0.73742412689) y(10) = [B]18,435.60[/B]

Pet supplies makes a profit of $5.50 per bag, if the store wants to make a profit of no less than $5225, how many bags does it need to sell? 5.5ob >= $5,225 Divide each side of the inequality by $5.50 b >=9.5 bags, so round up to a whole number of 10 bags.

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Prove 0! = 1 Let n be a whole number, where n! represents the product of n and all integers below it through 1. The factorial formula for n is: n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1 Written in partially expanded form, n! is: n! = n * (n - 1)! [U]Substitute n = 1 into this expression:[/U] n! = n * (n - 1)! 1! = 1 * (1 - 1)! 1! = 1 * (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

[URL='https://www.mathcelebrity.com/proofs.php?num=prove0%21%3D1&pl=Prove']Prove 0! = 1[/URL] Let n be a whole number, where n! represents: The product of n and all integers below it through 1. The factorial formula for n is n! = n · (n - 1) · (n - 2) · ... · 3 · 2 · 1 Written in partially expanded form, n! is: n! = n · (n - 1)! [SIZE=5][B]Substitute n = 1 into this expression:[/B][/SIZE] n! = n · (n - 1)! 1! = 1 · (1 - 1)! 1! = 1 · (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! ? 1 which contradicts the equation above [MEDIA=youtube]wDgRgfj1cIs[/MEDIA]

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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]

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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write 8 as a whole fraction Whole numbers can be written as whole number / 1 [B]8/1[/B]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number. [U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U] C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping C(s) = $6.50s + $50 + $25 C(s) = $6.50s + 75 [U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U] R(s) = Price Per Shirt * (s) Shirts R(s) = $15s [U]Step 3: Calculate Break-Even Point[/U] Break Even is where Cost = Revenue. Set C(s) = R(s) $6.50s + 75 = $15s [U]Step 4: Subtract 6.5s from each side[/U] 8.50s = 75 [U]Step 5: Solve for s[/U] [URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B]. [B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase? Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations: [LIST=1] [*]c + f = 10 [*]c + 1.5f = 12.50 [/LIST] Rearrange equation 1 by subtracting f from both sides: [LIST=1] [*]c = 10 - f [*]c + 1.5f = 12.50 [/LIST] Substitute equation (1) into equation (2): 10 - f + 1.5f = 12.50 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get: [B]f = 5[/B] Now, substitute this f = 5 value back into modified equation (1) above: c = 10 - 5 [B]c = 5[/B]