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

Round 98 to the nearest 10. This is 100. Call this a. Calculate b which is a - our original number: b = 100 - 98 b = 2 We can use this formula: (a - b)^2 = a(a- 2b) + b^2 Given a = 100 and b = 2, we have: (100 - 2)^2 = 100(100 - 2(2)) + 2^2 98^2 = 100(96) + 4 98^2 = 9600 + 4 98^2 = [B]9,604[/B] [MEDIA=youtube]8lQdxVVo-Ps[/MEDIA]

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]

9 times a number is that number minus 10 The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x: x 9 times a number means we multiply x by 9: 9x The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x: x That number minus 10 means we subtract 10 from x: x - 10 The word [I]is[/I] means equal to, so we set 9x equal to x - 10 [B]9x = x - 10[/B]

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage? [U]Calculate Sales Tax Amount:[/U] Sales Tax Amount = Total Bill - Original Cost Sales Tax Amount = 702 - 650 Sales Tax Amount = 52 [U]Calculate Sales Tax Percentage:[/U] Sales Tax Percentage = 100% * Sales Tax Amount / Original Cost Sales Tax Percentage = 100% * 52 / 650 Sales Tax Percentage = 100% * 0.08 Sales Tax Percentage = [B]8%[/B]

A 1975 comic book has appreciated 8% per year and originally sold for $0.26. What will the comic book be worth in 2020 Calculate the number of years: 2020 - 1975 = 45 Set up the accumulation function A(t) where t is the number of years since 1975: A(t) = 0.26(1.08)^t We want A(45) A(45) = 0.26(1.08)^45 A(45) = 0.26 * 32.9045 A(45) = [B]8.30[/B]

A boat is marked up 1/5 of the original price. The original price was $50. What is the new price of the boat 1/5 of 50 equals 10. So we add the markup of 10 to the original price of 50: 50 + 10 = [B]$60[/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 boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.25 he saved. How much money did he originally have? Find out what percent of money was spent Using a common denominator of 6, we have 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Therefore, 1/6 of his money is left to save. Let the boy's original money be x. We have: x/6 = 2.25 Cross multiply, we get x = [B]13.50[/B]

A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value of the car after 6 years? The Book Value depreciates 8% per year. We set up a depreciation equation: BV(t) = BV(0) * (1 - 0.08)^t The Book Value at time 0 BV(0) = 25,000. We want the book value at time 6. BV(6) = 25,000 * (1 - 0.08)^6 BV(6) = 25,000 * 0.92^6 BV(6) = 25,000 * 0.606355 BV(6) = [B]15,158.88[/B]

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle. Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C. C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning C = 13.4 + 1.6 C = [B]15 inches[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years? Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t: B(t) = 19,000(1-0.3)^t Simplifying this, we get: B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I] The problem asks for B(4): B(4) = 19,000(0.7)^4 B(4) = 19,000(0.2401) B(4) = [B]4,561.90[/B]

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

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters off the end. How long is the piece of wood now? When you saw off the end, the length decrease. So we subtract: New length = Original length - Sawed piec New length = 43.32 - 5.26 New length = [B]38.06[/B]

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price. How much is the computer now? We want 5/6 of 900. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=900&frac2=5/6&pl=Multiply']type this in our search engine[/URL] and we get: [B]750[/B]

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

A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough green dye is then poured into the cup to fill it again. What is the ratio of red to green to blue dye now? Original Cup: [LIST=1] [*]Blue [*]Green [*]Red [/LIST] Spilled Cup [LIST=1] [*]Empty [*]Blue [*]Green [*]Red [/LIST] Refilled Cup [LIST=1] [*]Green [*]Blue [*]Green [*]Red [/LIST] [B]1:4:1[/B]

A dress is on sale for $33. This is 3/5 of the regular price. What is the regular price? Original price is p. We have: 3p/5 = 33 Cross multiply using our [URL='http://www.mathcelebrity.com/prop.php?num1=3p&num2=33&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 55[/B].

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe? IF we subtract the $50 for the first 3 hours, we get: 110 - 50 = 60 remaining Each additional hour is 20, so the max number of hours we can rent the canoe is $60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy? Let p be the purchase price of pigs. We're given: [LIST] [*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C. [*]5 of them died, so he has p - 5 left [*]He sells 4(p - 5) pigs for a revenue amount R [*]Since profit is Revenue - Cost, which equals 56, we have: [/LIST] Calculate Profit P = R - C Plug in our numbers: 4(p - 5) - 232 = 56 4p - 20 - 232 = 56 To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get: p = [B]77[/B]

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction. Let the fraction be x/y. We're given two equations: [LIST=1] [*]x/y = 3/4 [*](x + 7)/y = 4/3. [I](The reciprocal of 3/4 is found by 1/(3/4)[/I] [/LIST] Cross multiply equation 1 and equation 2: [LIST=1] [*]4x = 3y [*]3(x + 7) = 4y [/LIST] Simplifying, we get: [LIST=1] [*]4x = 3y [*]3x + 21 = 4y [/LIST] If we divide equation 1 by 4, we get: [LIST=1] [*]x = 3y/4 [*]3x + 21 = 4y [/LIST] Substitute equation (1) into equation (2) for x: 3(3y/4) + 21 = 4y 9y/4 + 21 = 4y Multiply the equation by 4 on both sides to eliminate the denominator: 9y + 84 = 16y To solve this equation for y, we type it in our math engine and we get: y = [B]12 [/B] We then substitute y = 12 into equation 1 above: x = 3 * 12/4 x = 36/4 x = [B]9 [/B] So our original fraction x/y = [B]9/12[/B]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line. Our line equation is: y = mx + b We're given: m = 4/5 (x, y) = (0, 0) So we have: 0 = 4/5(0) + b 0 = 0 + b b = 0 Therefore, our line equation is: y = 4/5x [URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

A number multiplied by 6 and divided by 5 give four more than a number? A number is represented by an arbitrary variable, let's call it x. Multiply by 6: 6x Divide by 5 6x/5 The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4. 6x/5 = x + 4 Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side: 6x(5)/5 = 5(x + 4) The 5's cancel on the left side, giving us: 6x = 5x + 20 Subtract 5x from each side [B]x = 20[/B] Check our work from our original equation: 6x/5 = x + 4 6(20)/5 ? 20 + 4 120/5 ?24 24 = 24 <-- Yes, we verified our answer

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe is left? Calculate the length of cut pipe: 4 pieces * 33 inches per piece = 132 inches The remaining pipe is found by subtracting the original pipe length by the cut pipe length: 144 - 132 = [B]12 inches[/B]

A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to solve for t, we get: t = [B]18.85 years[/B] Note: if you need an integer answer, we round up to 19 years

[SIZE=4]A rectangle is cut in half to create two squares that each has an area of 25. What is the perimeter of the original rectangle? A. 20 B. 25 C. 30 D. 50[/SIZE] [SIZE=4]Area of a square: A = s^2 We're given A = 25: s^2= 25 s = 5 This means the rectangle width is 5. The rectangle length is 2(5) = 10. Perimeter of a rectangle: P = 2l + 2w P = 2(10) + 2(5) P = 20 + 10 P = [B]30 (choice C)[/B] [B][/B] [B][MEDIA=youtube]tKpS1gQY68o[/MEDIA][/B][/SIZE]

A salary after a 4.6% increase, of the original salary is x dollars 4.6% is also written as 0.046. Our formula for the new salary S is: S = (1 + 0.046)x [B]S = 1.046x[/B]

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would be its sale price? [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/5&pl=Multiply']1/5 of 45[/URL] = 9 45 - 9 = [B]36[/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 submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's original depth Below sea level is a negative amount. So they end up at -700. To go back up toward sea level, we'd be at: -700 + 132.58 = -567.42 Negative numbers mean below sea level, so the original depth was [B]567.42 meters below sea level[/B]

A tv is originally priced at $69.99 is reduced to $42.50. Find the % decrease in price Using our [URL='https://www.mathcelebrity.com/markup.php?p1=+69.99&m=+&p2=42.50&pl=Calculate']markdown calculator[/URL], we get: [B]-39.28%[/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 woman's original salary at a business was 3/4 her salary ten years later. If her salary after ten years is $50,000, what was her original salary? 450,000 * 3/4 = [B]$37,500[/B]

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price before the reduction? Using our [URL='http://www.mathcelebrity.com/markup.php?p1=++281.40&m=+33&p2=&pl=Calculate']markup/markdown calculator[/URL], we get: Original Sale Price = [B]$374.26[/B]

After buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to begin with? Let the beginning amount be b. We're given: b - 19 = 18. <-- [I]We subtract 19 because a purchase is a spend reducing the original amount[/I] To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-19%3D18&pl=Solve']type the equation b - 19 = 18 into our search engine [/URL]and we get: b = [B]37[/B]

After paying 7 dollars for the pie, Keith has 64 dollars left. How much money did he have before buying the pie? we add the 7 dollars back in to find Keith's original total t: t = 64 + 7 t = [B]$71[/B]

Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and each cup of coffee costs $2.50. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee. We start with 45, and each cup of coffee decreases our balance by 2.50, so we subtract: [B]A(x) = 45 - 2.50x[/B]

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage? Sales Tax = Tax Amount/Original Bill Sales Tax = 25.90/370 Sales Tax = 0.07 Multiply by 100 to convert to a percent, we have[B] 7%[/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number? The phrase [I]a number[/I] means an arbitrary variable, let's call it n. [LIST] [*]Start with n [*]Add 20 to it: n + 20 [*]Double it means we multiply the expression by 2: 2(n + 20) [*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53 [/LIST] 2(n + 20) = 53 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]6.5[/B]

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At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting? Let the original amount of money earned for babysitting be b. We're given: [LIST=1] [*]Start with b [*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65 [*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35 [*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b [/LIST] b - 14.65 - 1.35 = b/3 Multiply each side of the equation by 3 to remove the fraction 3(b - 14.65 - 1.35) = 3b/3 3b - 43.95 - 4.05 = b To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get: b =[B] 24[/B]

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, what was the total cost? 50% off of 50 means they pay half, or 1/2(50) = 25. Now, this gets taxed at 12%. So we multiply 25 * 1.12 Total Cost = 25(1.12) Total Cost = [B]$28[/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]

Free Chain Discounts and Net Cost Price and Net Cost Equivalent Calculator - Given a chain discount and an original price, this calculates the total discount and net cost price.

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]

Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number? Let the number be n. Divide by 8: n/8 Then add 1: n/8 + 1 The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2: n/8 + 1 = 2 To solve for n, we subtract 1 from each side to isolate the n term: n/8 + 1 - 1 = 2 - 1 Cancel the 1's on the left side, we get: n/8 = 1 Cross multiply: n = 8*1 n = [B]8[/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]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams? His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat. To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over. Therefore, he can consume: 17b <= 45 where b is the number of burgers Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

Each side of a square is lengthened by 3 inches . The area of this new, larger square is 25 square inches. Find the length of a side of the original square. area of a square is s^2 New square has sides s + 3, so the area of 25 is: (s + 3)^2 = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=%28s%2B3%29%5E2%3D25&pl=Solve']Solving for s[/URL], we get: s = [B]2[/B]

Eight workers dug 3/8 of a tunnel in 10 days. If they need to finish the remaining 5/8 of the tunnel in 3 & 1/3 days, how many more workers must they hire? Eight workers * 10 days = 80 days for one worker If 3/8 of a tunnel took 80 days for one worker, then each 1/8 of a tunnel takes a single worker: 80/3 = 26 & 2/3 days Multiply by 5 for the remaining 5/8 and we get: 133 & 1/3 We need 133 & 1/3 / 3 & 1/3 = 40 workers needed Additional workers = Workers Needed - Original Workers Additional workers = 40 - 8 Additional workers = [B]32[/B]

Expanded area = Original Area + area of Expansion Area of Expansion = length expansion * width expansion

In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?

Ok. To go further in this equation. It reads: ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Does that make sense to reverse 303? :-/ Thank you for your help!!

Let me post the whole equation paragraph: Brainteaser # 1: Answer for ACH A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits. What would the answer be?

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn’t stopped at the gas station and had driven along the diagonal path instead? [IMG]https://mathcelebrity.com/community/data/attachments/0/pythag-diagonal.jpg[/IMG] Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=14&side2input=48&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we see the diagonal route would be: 50 miles The original trip distance was: Original Trip Distance = 14 + 48 Original Trip Distance = 62 miles Diagonal Trip was 50 miles, so the difference is: Difference = Original Trip Distance - Diagonal Distance Difference = 62 - 50 Difference = [B]12 miles[/B]

Free Group Combinations Calculator - Given an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition.

a) 1800 is the cost to run the business for a day. To clarify, when you plug in x = 0 for 0 candy bars sold, you are left with -1,800, which is the cost of doing business for one day. b) Maximum profit is found by taking the derivative of the profit equation and setting it equal to 0. P'(x) = -0.002x + 3 With P'(x) = 0, we get: -0.002x + 3 = 0 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.002x%2B3%3D0&pl=Solve']equation solver[/URL], we get: x = 1,500 To get maximum profit, we plug in x = 1,500 to our [I]original profit equation[/I] P(1,500) = ? 0.001(1,500)^2 + 3(1,500) ? 1800 P(1,500) = -2,250 + 4,500 - 1,800 P(1,500) = $[B]450[/B]

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

If 72 is added to a number it will be 4 times as large as it was originally The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 72 added to a number: x + 72 4 times as large as it was originally means we take the original number x and multiply it by 4: 4x Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression: [B]x + 72 = 4x[/B] [B][/B] If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]24[/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 buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid? [U]Determine the monthly payment[/U] The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL] [U]Determine the total payments made[/U] Total payment is 36 times $114.87 = $4,135.37 [U]Now determine the total interest paid[/U] Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you triple a number and then add 10, you get one-half of the original number. What is the number? Let the number be n. We have: 3n + 10 = 0.5n Subtract 0.5n from each side 2.5n + 10 = 0 Subtract 10 from each side: 2.5n = -10 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2.5n%3D-10&pl=Solve']equation calculator,[/URL] we get: [B]n = -4[/B]

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy? Set up unit rate per plow: 14 hours * 3 plows = 42 hours for one plow to clear 500 miles of road Calculate the amount of plows we need: 42 hours / 6 hours = 7 plows Additional plows = New plows - original plows: Additional plows = 7 - 3 Additional plows = [B]4[/B]

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours? We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours: 3/4/1 = 3/p Dividing by 1 means the same as the original fraction, so we have: 3/4 = 3/p [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get: p = [B]4[/B]

It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how many additional painters must they hire? It takes one painter 4 * 12 hours = 48 hours to paint the house. Now we calculate the unit rate: 48 hours / 8 hours = 6 painters 6 painters - 4 original painters = [B]2 additional painters[/B]

Jacob bought a car that loses 10% of its value each year. If the original cost of the car is n dollars, what is its value after 3 years? [LIST] [*]Year 1: 0.9*n = 0.9n [*]Year 2: 0.9 * 0.9n = 0.81n [*]Year 3: 0.9 * 0.81n = [B]0.729n[/B] [/LIST]

Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What was the original number? Let the original number be n. [LIST=1] [*]Add -12: n - 12 [*]Subtract -9: n - 12 - -9 = n - 12 + 9 [*]Add 8: n - 12 + 9 + 8 [*]Subtract - 2: n - 12 + 9 + 8 - -2 = n - 12 + 9 + 8 + 2 [*]The result is -5. So we build the following equation: [/LIST] n - 12 + 9 + 8 + 2 = -5 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-12%2B9%2B8%2B2%3D-5&pl=Solve']type it in our search engine[/URL] and we get: [B]n = -12[/B]

Jim was thinking of a number. Jim adds 20 to it, then doubles it and gets an answer of 99.2. What was the original number? Start with x. Add 20 to it x + 20 Double it 2(x + 20) Set this equal to 99.2 2(x + 20) = 99.2 Divide each side by 2: x + 20 = 49.6 Subtract 20 from each side: x = [B]29.6[/B]

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average. Let A be the original average. The new average is: A + (-10)

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

Find what was used: Used Money = Prepaid original cost - Remaining Credit Used Money = 20 - 17.47 Used Money = 2.53 Using (m) as the number of minutes, we have the following cost equation: C(m) = 0.11m C(m) = 2.53, so we have: 0.11m = 2.53 Divide each side by 0.11 [B]m = 23[/B]

Let us take an integer x which is both even [I]and[/I] odd. [LIST] [*]As an even integer, we write x in the form 2m for some integer m [*]As an odd integer, we write x in the form 2n + 1 for some integer n [/LIST] Since both the even and odd integers are the same number, we set them equal to each other 2m = 2n + 1 Subtract 2n from each side: 2m - 2n = 1 Factor out a 2 on the left side: 2(m - n) = 1 By definition of divisibility, this means that 2 divides 1. But we know that the only two numbers which divide 1 are 1 and -1. Therefore, our original assumption that x was both even and odd must be false. [MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

Ruth has already jarred 3 liters of jam and will jar an additional 1 liter of jam everyday. How much jam did Ruth jar if she spent 7 days making jam? 7 days at 1 liter = 7 x 1 = 7. Add that 7 to our original 3 and we have, 7 + 3 = 10 liters of jam.

We know the following: [LIST] [*]csc(x) = 1/sin(x) [*]sec(x) = 1/cos(x) [*]cot(x) = 1/tan(x) [/LIST] We can rewrite our original expression as: sin(x) * cos(x) * tan(x)/sin(x) * cos(x) * tan(x) Everything cancels and we are left with [B]1[/B] [MEDIA=youtube]MsL-Ni4Hen4[/MEDIA]

We know from the pythagorean theorem: [SIZE=5][B]sin^2(x) + cos^2(x) = 1[/B] [B]Subtract sin^2(x) from each side and we get:[/B] [B][B]cos^2(x) = 1 - [B]sin^2(x)[/B][/B][/B] [B][B][B]We can rewrite our original expression as:[/B][/B][/B] [B][B][B]sin^2(x)/cos^2(x)[/B][/B][/B] [/SIZE] [B][B][B][SIZE=5]But this expression [/SIZE][SIZE=4]equals[/SIZE][SIZE=5] tan^2(x)[/SIZE][/B][/B][/B] [MEDIA=youtube]zqYg0VRq5Ak[/MEDIA]

Steve woke up and it was -12 Fahrenheit outside the weatherman said it was supposed to warm up to 20 degrees. how many degrees will the temperature increase We start with a temperature of -12F Warming up means we [U][B]add[/B][/U] degrees to the original temperature. -12 + 20 = [B]+8F[/B]

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Suppose a city's population is 740,000. If the population grows by 12,620 per year, find the population of the city in 7 years. We setup the population function P(y) where y is the number of years of population growth, g is the growth per year, and P(0) is the original population. P(y) = P(0) + gy Plugging in our numbers of y = 7, g = 12,620, and P(0) = 740,000, we have: P(7) = 740,000 + 12,620 * 7 P(7) = 740,000 + 88,340 P(7) = [B]828,340[/B]

The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction. Let the original fraction be n/d. We're given: [LIST=1] [*]d = n + 4 [*](n + 4) / (d + 7) = 1/2 [/LIST] Cross multiply Equation 2: 2(n + 4) = d + 7 2n + 8 = d + 7 Now substitute equation (1) into tihs: 2n + 8 = (n + 4) + 7 2n + 8 = n + 11 [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get: n = 3 This means from equation (1), that: d = 3 + 4 d = 7 So our original fraction n/d = [B]3/7[/B]

The expression (5x - 2)/(x + 3) is equivalent to which of the following? [LIST] [*]A) (5 - 2)/3 [*]B) 5 - 2/3 [*]C) 5 - (2/(x + 3)) [*]D) 5 - (17/(x + 3)) [/LIST] Let's start with an integer x = 2. Plug that into our original expression, and we get: (5(2) - 2)(2 + 3) (10 - 2)/5 8/5 So what we do next is, take x = 2, and plug it into answer choices A-D, and see which one results in 8/5 A) 3/3 = 1 <-- Nope B) Since 5 is 15/3, we have 15/3 - 2/3 = 13/3 which is over 4, so Nope C) 5 - (2/(2 + 3)) = 5 - (2/5). Since 5 is 25/5, we have 25/5 - 2/5 = 23/5. <-- Nope D) 5 - (17/(2 + 3)) = 5 - 17/5. Since 5 is 25/5, we have 25/5 - 17/5 = 8/5 <-- YES Since 8/5 = 8/5, our answer is [B]D) 5 - (17/(x + 3))[/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 perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle. l = 4w - 15 Perimeter = 2l + 2w Substitute, we get: 400 = 2(4w - 15) + 2w 400 = 8w - 30 + 2w 10w - 30 = 400 Add 30 to each side 10w = 370 Divide each side by 10 to isolate w w = 37 Plug that back into our original equation to find l l = 4(37) - 15 l = 148 - 15 l = 133 So we have (l, w) = (37, 133)

The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers. Let x = the original positive integer. We have: [LIST] [*]Consecutive integer is x + 1 [*]x^2 - 2(x + 1) = 22 [/LIST] Multiply through: x^2 - 2x - 2 = 22 Subtract 22 from each side: x^2 - 2x - 24 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2-2x-24%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x = 6 and x = -4 Since the problem states [U]positive integers[/U], we use: x = 6 and x + 1 = 7 [B](6, 7)[/B]

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number? Let x and (16-x) represent the original ten and units digits respectively Reversing its digits increases the number by 18 Set up the relational equation [10x + (16-x)] + 18 = 10(16 - x) + x Solving for x 9x + 34 = 160 - 9x Combine like terms 18x = 126 Divide each side of the equation by 18 18x/18 = 126/18 x = 7 So 16 - x = 16 - 7 = 9 The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up. The number in our answer is [B]79[/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]

When the side of a square is doubled in length, its area increases by 432 square inches. What is the size of the original square? Original square side length is s Area = s^2 Double the side lengths to 2s New area = (2s)^2 = 4s^2 Setup the difference relation: 4s^2 - s^2 = 432 3s^2 = 432 Divide each side by 3: 3s^2/3 = 432/3 s^2 = 144 s = [B]12[/B]

Yolanda had 9 cookies in a jar. She then bought 6 bags of 13 cookies each. How many cookies does she have now? 6 bags * 13 cookies each = 78 cookies. 78 cookies added to the original 9 in the jar = [B]87 cookies[/B].

You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food. Our purchase includes at cat litter and cat food. Adding those together, we're given: 12.25 + x = 19.08 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get: x = 6.83 Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price. Original purchase price = After tax price / (1 + tax rate) Original purchase price = 6.83/1.06 Original purchase price = [B]$6.44[/B]

you start at a point on the number line and move 4 units left. If you are now at 10, then what was your original point? Work backwards. If we're at 10, and we moved left, this means we add 4 to get back to our starting point: 10 + 4 = [B]14[/B]