2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve. Set up our 2 equations where cost = price * quantity: [LIST=1] [*]2x + y = 35 [*]3x + 4y = 65 [/LIST] We can solve this one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]x (cost of 1 pen) = 15[/B] [*][B]y (cost of 1 eraser) = 5[/B] [/LIST]

2 tons of dirt cost $280.00. What is the price per pound? We know that 1 ton = 2000 pounds. So 2 tons = 2*2000 = 4,000 pounds We rewrite this as 4,000 pounds of dirt cost $280.00. We set up a proportion where p is the price per one pound: 4000/280 = 1/p [URL='https://www.mathcelebrity.com/prop.php?num1=4000&num2=1&den1=280&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this in our search engine[/URL], we get: p = [B]0.07 or 7 cents per pound.[/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]

$69.99 per apple / 200 apples We want the price per apple. Divide top and bottom by 200 $0.35 per apple.

3 cartons of eggs for $5 what if the cost of 8 cartons Set up a proportion of cartons of eggs to price where p is the price of 8 cartons: 3/5 = 8/p [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=8&den1=5&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get: p = [B]13.33[/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 tons of compost cost $3,600.00. What is the price per pound? 1 ton = 2000 pounds, so 3 tons is: 3 * 2000 = 6000 pounds Price per pound = Cost / Total pounds Price per pound = 3600 / 6000 Price per pound = [B]$0.60 per pound[/B]

4 adults and 3 children cost $40. Two adults and 6 children cost $38 Givens and Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of children be c [*]Cost = Price * Quantity [/LIST] We're given 2 equations: [LIST=1] [*]4a + 3c = 40 [*]2a + 6c = 38 [/LIST] We can solve this system of equations 3 ways [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get: [LIST] [*][B]a = 7[/B] [*][B]c = 4[/B] [/LIST]

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: [LIST=1] [*]a + c = 414 [*]2a + 1.75c = 755.25 [/LIST] We have a simultaneous equations. You can solve this any of 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] Whichever method you choose, you get the same answer: [LIST] [*][B]a = 123[/B] [*][B]c = 291[/B] [/LIST]

5 chocolates cost $25. What will 15 chocolates cost? Set up a proportion of chocolates to cost, where p is the price of 15 chocolates: 5/25 = 15/p Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=15&den1=25&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 75[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of kids be k [/LIST] Given with assumptions: [LIST=1] [*]a + k = 508 [*]2a + 1.25k = 885.50 (since cost = price * quantity) [/LIST] Rearrange equation (1) by subtracting c from each side to isolate a: [LIST=1] [*]a = 508 - k [*]2a + 1.25k = 885.50 [/LIST] Substitute equation (1) into equation (2): 2(508 - k) + 1.25k = 885.50 Multiply through: 1016 - 2k + 1.25k = 885.50 1016 - 0.75k = 885.50 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]174[/B] Now, to solve for a, we substitute k = 174 into equation 1 above: a = 508 - 174 a = [B]334[/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 2-quart carton of sour cream costs $7.96. What is the price per pint? Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=2&pl=Calculate&type=quart']conversion calculator[/URL]: 2 quarts = 4 pints $7.96/4 pints = [B]$1.99 per pint[/B]

A 3 gallon bottle of bleach cost $16.32. What is the price per cup? We're given 16.32 / 3 gallons Divide the top and bottom of the fraction by 3 to get the cost per gallon: 16.32/3 = 5.44 gallon Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']measurement converter[/URL], we see that: 1 gallon = 16 cups So 5.44 /16 cups=[B]$0.34 per cup[/B]

A 3-gallon bucket of paint costs $87.12. What is the price per quart? 3 gallons equals 12 quarts with our [URL='https://www.mathcelebrity.com/liqm.php?quant=3&pl=Calculate&type=gallon#quart']conversion calculator[/URL]. We divide 87.12 for 12 quarts by 12: [URL='https://www.mathcelebrity.com/perc.php?num=87.12&den=12&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']87.12 / 12[/URL] = [B]$7.26 per quart[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800? Let x be the number of $24 tickets, and y be the number of $40 tickets. We have: [LIST=1] [*]24x + 40y = 188,800 [*]x + y = 6,000 [*]Rearrange (2) to solve for x: x = 6000 - y [*]Plug in (3) to (1): [/LIST] 24(6000 - y) + 40y = 188800 144,000 - 24y + 40y = 188,800 16y + 144,000 = 188,800 Subtract 144,000 from each side: 16y = 44,800 Divide each side by 16 y = 2,800 ($40 tickets) Plug this into (2) x + 2,800 = 6000 Subtract 2,800 from each side: x = 3,200 ($24 tickets)

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch? Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that: 7 feet = 84 inches So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&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']divide $3.36 by 84[/URL] to get the cost per inch: $3.36/84 = [B]0.04 per inch[/B]

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen? 1 dozen = 12 muffins What this problem is really asking, $3.50 for 4 muffins. Let p be the price for 12 muffins (1 dozen). Set up a proportion of cost to muffins. 3.50/4 = p/12 Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=3.50&num2=p&den1=4&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get: p = [B]10.5 muffins [MEDIA=youtube]ccY7yDkKvzs[/MEDIA][/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ? 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ? 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ? 252.4.5 [B]t ? 56[/B]

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale? [U]Calculate the sale price:[/U] Sale Price = Normal Price * (1 - Sales Percentage) [U]With our sales percentage of 15% = 0.15, we have:[/U] Sale Price = 1100 * (1 - 0.15) Sale Price = 1100 * (0.85) Sale Price = 935 [U]Calculate post tax amount:[/U] Post tax amount = Sale Price * (1 + Tax Percentage) [U]With our tax percentage of 2% = 0.02, we have:[/U] Post tax amount = 935 * (1 + 0.02) Post tax amount = 935 * (1.02) Post tax amount = [B]$953.70[/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 bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even? Profit = Revenue - Cost Let the number of bikes be b. Revenue = 80b Cost = 60b + 1500 Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other: 60b + 1500 = 80b We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]75[/B]

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

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

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss. [U]Since sale price is less than purchase price, we have a loss:[/U] Loss = Sale Price - Purchase Price Loss = 150 - 200 Loss = -50 [U]Calculate percent loss:[/U] Percent Loss = 100% * Loss / Purchase Price Percent Loss = 100% * -50/200 Percent Loss = 100% *- 1/4 Percent Loss = [B]-25%[/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 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 boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be? Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece: [LIST=1] [*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer) [*]m = s + 6 [*]s + m + l = 57 [/LIST] We substitute equations (1) and (2) into equation (3): s + (s + 6) + (s + 9) = 57 Group like terms: (1 + 1 + 1)s + (6 + 9) = 57 3s + 15 = 57 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]14 [/B] [U]Plug s = 14 into equation 2 to solve for m:[/U] m = 14 + 6 m = [B]20 [/B] [U]Plug s = 14 into equation 1 to solve for l:[/U] l = 14 + 9 l = [B]23 [/B] Check our work for equation 3: 14 + 20 + 23 ? 57 57 = 57 <-- checks out [B][/B]

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the software? Let c be the cost of the computer and s be the cost of the software. We have two equations: [LIST=1] [*]c + s = 4000 [*]c = 4s [/LIST] Substitute (2) into (1) (4s) + s = 4000 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D4000&pl=Solve']equation solver[/URL], we get [B]s = 800[/B]. Substitute this into Equation (2), we get: c = 4(800) [B]c = 3,200[/B]

A car is bought for $2400 and sold one year later $1440 find the loss as a percentage of the cost price. (2400 - 1440)/2400 960/2400 0.4 As a percentage, we multiply by 100 to get [B]40%[/B]

a car was bought for $24300 and sold at a loss of $2290. Find the selling price. A loss means the car was sold for less than the buying price. Let the selling price be S. we have: 24300 - S = 2290 [URL='https://www.mathcelebrity.com/1unk.php?num=24300-s%3D2290&pl=Solve']Typing this equation into our search engine[/URL], we get: s = [B]22,010[/B]

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a person have to play to spend at least $40? Let g be the number of games. The Spend function S(g) is: S(g) = Cost per game * number of games + admission price S(g) = 4g + 15 The problem asks for g when S(g) is at least 40. At least is an inequality using the >= sign: 4g + 15 >= 40 To solve this inequality for g, we type it in our search engine and we get: g >= 6.25 Since you can't play a partial game, we round up and get: [B]g >= 7[/B]

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters of the value at the beginning of the year. Write the first four terms of the sequence of the car’s value at the end of each year. three-quarters means 3/4 or 0.75. So we have the following function P(y) where y is the number of years since purchase price: P(y) = 24000 * 0.75^y First four terms: P(1) = 24000 * 0.75 = [B]18000[/B] P(2) = 18000 * 0.75 = [B]13500[/B] P(3) = 13500 * 0.75 = [B]10125[/B] P(4) = 10125 * 0.75 = [B]7593.75[/B]

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find the expected value. Expected Value E(x) is: E(x) = Probability of winning * Winning Price - Probability of losing * Ticket Price [U]Since only 1 cash price will be given, 2299 will be losers:[/U] E(x) = 4600 * (1/2300) - 2299/2300 * 7 E(x) = 2 - 0.99956521739 * 7 E(x) - 2 - 7 E(x) = [B]-5[/B]

A certain textbook cost $94. If the price increases each year by 3% of the previous year's price, find the price after 7 years. Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?num=acertaintextbookcost94.ifthepriceincreaseseachyearby3%ofthepreviousyearspricefindthepriceafter7years&pl=Calculate']appreciation calculator[/URL], we get: [B]115.61[/B]

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression to represent the sale price of the coat. Show your work. The Sale price of the coat is: S = p(1 - 0.35) <-- Since 35% is 0.35 as a decimal [B]S = 0.65p[/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 company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order? [U]Set up Cost function C(t) where t is the number of tapestries:[/U] C(t) = Cost per tapestry * number of tapestries + Fixed Cost C(t) = 34t + 26000 [U]Set up Revenue function R(t) where t is the number of tapestries:[/U] R(t) = Sale Price * number of tapestries R(t) = 63t [U]Set up Profit function P(t) where t is the number of tapestries:[/U] P(t) = R(t) - C(t) P(t) = 63t - (34t + 26000) P(t) = 63t - 34t - 26000 P(t) = 29t - 26000 [U]The problem asks for profit when t = 2400:[/U] P(2400) = 29(2400) - 26000 P(2400) = 69,600 - 26,000 P(2400) = [B]43,600[/B]

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15 Set up the cost function C(u) where u is the number of units is: C(u) = Cost per unit * u + Fixed Cost C(u) = [B]6u + 34000[/B] Set up the revenue function R(u) where u is the number of units is: R(u) = Sale price per unit * u R(u) = [B]15u[/B]

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x . [U]Set up the cost function C(x):[/U] C(x) = Cost per product * x + Fixed Costs C(x) = 293x + 474778 [U]Set up the Revenue function R(x):[/U] R(x) = Sale Price * x R(x) = 820x [U]Set up the Profit Function P(x):[/U] P(x) = Revenue - Cost P(x) = R(x) - C(x) P(x) = 820x - (293x + 474778) P(x) = 820x - 293x - 474778 [B]P(x) = 527x - 474778[/B]

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

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55. [U]The cost function for "u" uniforms C(u) is given by:[/U] C(u) = Cost per uniform * u + Fixed Costs [B]C(u) = 15u + 640[/B] Build the revenue function R(u) where u is the number of uniforms: R(u) = Sale Price per uniform * u [B]R(u) = 55u[/B] Calculate break even function: Break even is where Revenue equals cost C(u) = R(u) 15u + 640 = 55u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]16 So we break even selling 16 uniforms[/B]

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

A 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 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 coupon that was mailed to preferred customers of video village rentals is good for 15% on any video that is bought. How much savings is there using the coupon to purchase a $22 video? Savings = Full Price * Coupon Amount Savings = $22 * 0.15 Savings = $3.30

A deck of cards costs f dollars. If Sharon bought 9 decks of cards, how much did she spend? Calculate Total Cost: Total Cost = Decks of Cards * Price per deck Total Cost = [B]9f[/B]

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each find the percentage mark up Find Unit Cost: Unit Cost = Cost / Number of Shirts Unit Cost = 600 / 100 Unit Cost = 6 With a selling price of 10, our markup percentage is: Markup % = 100 * (New Price - Old Price)/Old Price Markup % = 100 * (10 - 6)/6 Markup % = 100 * 4/6 Markup % = 400/6 Markup % = [B]66.67%[/B]

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost of the cat? Set up givens and equations [LIST] [*]Let the cost of the dog be d [*]Let the cost of the cat be c [/LIST] We're given 2 equations: [LIST=1] [*]c + d = 100 [*]d = c + 90 [/LIST] Substitute equation (2) into equation (1) for d c + c + 90 = 100 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2Bc%2B90%3D100&pl=Solve']math engine[/URL], we see that: c = [B]5 [/B] Substitute c = 5 into equation (2) above: d = 5 + 90 d = [B]95[/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 buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy? Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee: 167t + 19t + 16 = 1132 Combine like terms: 186t + 16 = 1132 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have: [B]t = 6[/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 girl bought a skirts at $30 each and j jerseys at $15 each at a total cost of $285. Since cost = price * quantity, we have: [B]30a + 15j = 285[/B]

A grocery store sells 6 pounds of apples for $12. What is the unit price of the apples? Unit Price = Cost/Quantity Unit Price = 12/6 [B]Unit Price = $2/lb[/B]

A hoodie sold for d dollars. Now, the new price of the hoodie can be represented by 1.3d. Which description could explain what happened to the price of the hoodie? We can rewrite this as: d(1 + 0.3) And in this format, we see that the [B]hoodie was increased by 30% [/B]which is also 1.3

A hot dog costs $3 and a corn dog costs $1.50. If $201 was collected, write a mathematical sentence to represent this information Assumptions: [LIST] [*]Let the number of corn dogs be c [*]Let the number of hot dogs be h [/LIST] Since cost = price * quantity, we have: [B]1.50c + 3h = 201[/B]

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll away bed. Your family rents a house for a week and pays $756. How many roll away beds did they rent? Roll Away Beds = (Total Rental Price - Weekly Charge)/Per night bed fee Plugging in our numbers, we get: Roll Away Beds = (756 - 700)/4 Roll Away Beds = 56/4 Roll Away Beds = [B]14[/B]

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the commission rate. Commission Rate = 100 * Commission Amount / Sale Price Commission Rate = 100 * 10200/20000 Commission Rate = 100 * 0.051 Commission Rate = [B]5.51%[/B]

A kilogram of rice costs $2.05.what is the cost of 30kg of the rice? We multiply the price for 1 kilogram by the 30 kilograms total: $2.05 * 30 = [B]$61.50[/B]

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5. Set up the expected values E(x): for the 1,000 price: E(x) = (1000 - 5) * 1/1000 = 995/1000 For the 5 $100 prizes: E(x) = (100 - 5) * 5/1000 = 475/1000 For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets: E(x) = -3 * 994/1000 = -2982/1000 We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators: E(x) = (995 + 475 - 2982)/1000 E(x) = -1512/1000 E(x) = [B]-1.51[/B]

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of the cost price Calculate Profit: Profit = Sales Price - Cost Profit = 1000 - 800 Profit = 200 Calculate profit percentage: Profit Percentage = Profit * 100 / Cost Profit Percentage = 800 * 100 / 200 Profit Percentage = [B]400%[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

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

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

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 each. In all she spent $387. How many of the cheaper calculators did she buy Let the number of cheaters calculators be c. Since amount equals price * quantity, we're given the following equation: 8.20 * 40 + 2.95c = 387 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=8.20%2A40%2B2.95c%3D387&pl=Solve']type it in our search engine [/URL]and we get: c = [B]20[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs. Let the number of songs be s. And the cost function be C(s). We have: C(s) = Price per song downloaded * s + app download charge C(s) = 1.29s + 2 The problem asks for C(30): C(3) = 1.29(30) + 2 C(3) = 38.7 +2 C(3) = $[B]40.7[/B]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000 Step 1, the question asks for Book Value. Let y be the number of years since purchase. We setup an equation B(y) which is the Book Value at time y. B(y) = Sale Price - Depreciation Amount * y We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000 30000 - 3000y = 9000 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get: y = [B]7 [/B] To check our work, substitute y = 7 into B(y) B(7) = 30000 - 3000(7) B(7) = 30000 - 21000 B(7) = 9000 [MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

A pack of 12 tortillas cost $3.24. What is the price per tortilla? Price per tortilla = Total Cost / Total Tortillas Price per tortilla = $3.24/12 Price per tortilla = [B]$0.27[/B]

A pack of 36 black sharp tip markers costs $34.49. What is the price of one marker? Set up unit cost: 34.49/36 = [B]$0.96 per marker[/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 shoes cost $250. The price was decreased by 20%. A week later shoes were mark down again by 25%. What is the final price of the shoes? 20% is 0.2. 25% is 0.25. A decrease is a reduction, so we have: Final Price = 250 * (1 - 0.2) * (1 - 0.25) Final Price = 250 * 0.8 * 0.75 Final Price = [B]150[/B]

A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv at a markup of 20%. If he makes a profit of $165 on the sale of the two items, what did he pay for the computer? Let c be the price of the computer and t be the price of the tv. WE have: [LIST=1] [*]c + t = 600 [*]c(1.3) + t(1.2) = 765 <-- (600 + 165 profit) [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+600&term2=1.3c+%2B+1.2t+%3D+765&pl=Cramers+Method']simultaneous equation calculator[/URL], we get: [B]c = 450[/B] t = 150

A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $50. What was her profit or loss She lost, since the sale price was less than the purchase price. The loss is calculated as: 50 - 60 = [B]-$10[/B]

A piece of gym equipment which cost 450 including vat last year is now selling at 500 excluding vat. Calculate the percentage increase. Increase = (New Price - Old Price)/Old Price Increase = (500-450)/450 50/450 = 0.1111 To get the percentage, multiply by 100 [B]11.11%[/B]

a popcorn is $7.00 and a drink is $3.50 tax is 7%. how much will I pay? Calculate pre-tax amount: Pre-tax amount = Popcorn price + drink price Pre-tax amount = 7 + 3.50 Pre-tax amount = $10.50 Calculate post-tax amount: Post-tax amount = Pre-tax amount * (1 + tax percent/100) Post-tax amount = $10.50* (1 + 7/100) Post-tax amount = $10.50 * 1.07 Post-tax amount = [B]$11.24[/B]

a pound of chocolate cost 7 dollars. Raina pays p pounds Cost = Price * Quantity, so we have: Cost =[B] 7p [/B]

A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total cost c that Greg pays Since cost = price * quantity, we have: [B]c = 6p[/B]

A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total cost c that Ryan pays Since cost = Price * Quantity, we have: [B]c = 6p[/B]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80. [U]Build the cost function C(b) where b is the number of bags of pretzels:[/U] C(b) = Cost per bag * b + Fixed Costs C(b) = 0.70b + 1100 [U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U] R(b) = Sale price * b R(b) = 1.80b [U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U] P(b) = Revenue - Cost P(b) = R(b) - C(b) P(b) = 1.80b - (0.70b + 1100) P(b) = 1.80b = 0.70b - 1100 P(b) = 1.10b - 1100

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% of the total commission. How much will the listing salesperson receive if she is paid 60% of the amount retained by listed broker. [U]Calculate commission amount:[/U] Commission amount = Sale Price * Commission Percent Commission amount = 198,000 * 8% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=8&den1=198000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Commission amount [/URL]= 15,840 [U]Calculate listing salesperson commission amount:[/U] Listing salesperson commission amount = Commission Amount * Listing salesperson Percent Listing salesperson commission amount = 15,840 * 60% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=15840&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Listing salesperson commission amount[/URL] = [B]9,504[/B]

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets 45% of this commission. How much money does the agent get? The agents Commission (C) is: C = Sale price * sales commission percent * agent commission percent Since 6% = 0.06 and 45% = 0.45, we have: C = 229605 * 0.06 * 0.45 C = [B]6,199.34[/B]

a repairman charged $93.06. The price included 2 hours of labor and a $40 service charge. How much does the repairman charge per hour? Subtract the service charge: 93.06 - 40 = 53.06 53.06/2 hours = [B]$26.53 per hour[/B].

A restaurant is going to raise all their prices by 5%. If the current price of an item is p dollars, write an expression for the price after the increase. 5% = 0.05 as a decimal. New price = Old Price * (1 + decimal increase) New price = p * (1 + 0.05) New price = [B]1.05p[/B]

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars, write an expression for the price after the increase. A 7% increase on price means we multiply the current price of p by 1.07. So our algebraic expression is: [B]1.07p[/B]

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate. Write your answer as a percentage. Commission percentage = Commission Amount / Sales Price Commission percentage = 364 / 2600 Commission percentage = 0.14 Multiply by 100 to get the percentage: 0.14 * 100 = [B]14%[/B]

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold? Set up the cost equation C(x) where x is the number of plates sold: C(x) = Cost per plate * x plates C(x) = 2x Set up the revenue equation R(x) where x is the number of plates sold: R(x) = Sales price per plate * x plates C(x) = 8x Set up the profit equation P(x) where x is the number of plates sold: P(x) = R(x) - C(x) P(x) = 8x - 2x P(x) = 6x We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x: 6x = 2400 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3D2400&pl=Solve']type it in our math engine[/URL] and we get: x =[B]400 plates[/B]

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even? [U]Set up the cost function C(p) where p is the number of pieces of candy.[/U] C(p) = Cost per piece * p + shipping and handling fee C(p) = 0.2p + 9 [U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U] R(p) = Sale price * p R(p) = 0.5p Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function 0.2p + 9 = 0.5p To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get: p = [B]30[/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 shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts. Cost equals quantity times price, so we have the total cost C: [B]C(s, j) = 15s + 25j[/B]

A shoe store was having a sale where 2 pairs of Brand A shoes cost $23.10 and 3 pairs of Brand B shoes cost $35.85. Which brand is the better buy? [URL='https://www.mathcelebrity.com/betterbuy.php?p1=23.10&p2=35.85&q1=2&q2=3&pl=Better+Buy']Using our better buy calculator[/URL]: [SIZE=5][B]Calculate Unit Price[/B][/SIZE] Unit Price = Price/Quantity [SIZE=5][B]Calculate Unit Price 1:[/B][/SIZE] Unit Price Brand A = P1/Q1 Unit Price Brand A = 23.10/2 Unit Price Brand A = 11.55 [SIZE=5][B]Calculate Unit Price 2:[/B][/SIZE] Unit Price Brand B = P2/Q2 Unit Price Brand B = 35.85/3 Unit Price Brand B = 11.95 Since Brand A's Unit price is lower, [B]Brand A is the better buy [MEDIA=youtube]Q16iZn6Uer8[/MEDIA][/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 shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out his percentage profit. [U]Calculate Revenue[/U] Revenue = Sale price per can * number of cans Revenue = 0.65 * 20 Revenue = 13 [U]Calculate Profit given a cost of $10:[/U] Profit = Revenue - Cost Profit = 13 - 10 Profit = 3 [U]Calculate Percentage Profit:[/U] Percentage Profit = Profit/Revenue * 100% Percentage Profit = 3/13 * 100% Percentage Profit = 0.23076923076 * 100% Percentage Profit = [B]23.08%[/B]

A soda cost $100. What is the cost of y sodas? Total cost = price * quantity Total Cost = [B]100y[/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 sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt? State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5: 5s = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get: s = [B]8[/B]

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales tax of 4% on the item, do you have enough to buy the sweater? Calculate after-tax amount: After tax amount = Sale Price * (1 + sales tax percent) After tax amount = 32 * (1 + 0.04) <-- Since 4% = 0.04 After tax amount = 32 * (1.04) After tax amount = $33.28 [B]Yes[/B], since $33.28 is less than or equal to $35, you have enough to buy the sweater.

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for children. If the total proceeds were $13,930 for a sold- out matinee, how many of each type of ticket were sold? Let a be the number of adult tickets and c be the number of children tickets. We have the following equations: [LIST=1] [*]a + c =459 [*]53a + 16c = 13930 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D459&term2=53a+%2B+16c+%3D+13930&pl=Cramers+Method']simultaneous equation calculator[/URL], we have: [B]a = 178 c = 281[/B]

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even? [U]Set up the cost function C(b) where b is the number of bears:[/U] C(b) = Cost per bear * b + factory expenses C(b) = 8b + 1500 [U]Set up the revenue function R(b) where b is the number of bears:[/U] R(b) = Sale Price per bear * b R(b) = 12b [U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U] C(b) = R(b) 8b + 1500 = 12b To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]375[/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 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]

A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks. Cost = Price * Quantity, so we have: [B]2.50x + 0.50f[/B]

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.20 per foot for the next 10 feet, and so on, at a price increase of $0.10 per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet? Set up the cost function C(f) where f is the number of feet: Cost = 9(10) + 9.1(10) + 9.2(10) + 9.3(10) + 9.4(10) + 9.5(10) + 9.6(10) + 9.7(10) + 9.8(10) + 9.9(10) + 10(10) + 10.1(10) + 10.2(10) + 10.3(10) + 10.4(10) Cost = [B]1,455[/B]

Aaron bought a guitar for n dollars. The tax in his state is 6%. What is the total cost of the guitar including tax? Sale price is n Tax on sale is 0.06n Add them together n + 0.06n = [B]1.06n[/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]

Ali buys 6 sunglasses which cost $1.84 each, calculate the total cost. Total Cost = Quantity * Price Total Cost = 6 * $1.84 Total Cost = [B]$11.04[/B]

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=8.52&p2=9.98&q1=36&q2=48&pl=Better+Buy']better buy calculator[/URL], we see the following unit prices: [LIST] [*][B]Brand A = $0.24[/B] [*][B]Brand B = $0.21[/B]. [*][B]Brand B has the better unit price by 3 cents.[/B] [/LIST]

Assume you have a laptop worth 2900. There is a 3 percent chance of it getting lost what’s the fair premium insurance? Fair premium Insurance = Price * probability of loss: Fair premium Insurance = 2,900 * 3% Fair premium Insurance = [B]87[/B]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold? Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations: [LIST=1] [*]c = a + 30 [*]6a + 4c = 6360 [/LIST] Substitute equation (1) into equation (2): 6a + 4(a + 30) = 6360 Multiply through to remove parentheses: 6a + 4a + 120 = 6360 T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get: a = 624 Now substitute a = 624 back into equation (1) to solve for c: c = 124 + 30 c = [B]154[/B]

At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cost of ride tokens and let y represent the cost of game tokens. Write an equation in standard for that can be used to determine how much each type of token costs. We know that: Token Cost + Game Cost = Total Cost Since cost = price * quantity, we have: [B]5x + 9y = 59[/B]

At Costco, a case of 12 boxes of macaroni and cheese costs $18.00. How much is each box of macaroni and cheese worth? Cost per box = Total price / number of boxes Cost per box = $18/12 Cost per box = [B]$1.50[/B]

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use. [U]Define variables[/U] [LIST] [*]Let c be the number of corn plants [*]Let p be the number of potato plants [/LIST] Since cost = price * quantity, we're given two inequalities: [LIST=1] [*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B] [*][B]c + p < 15[/B] [/LIST]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil The cost per pencil is: 1560/30 = 52 Build revenue function: Revenue = Number of Pencils * Sales Price (s) Revenue = 30s The profit equation is: Profit = Revenue - Cost Given profit is 180 and cost is 1560, we have: 30s - 1560 = 180 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get: s = 58 This is sales for total profit. The question asks profit per pencil. Profit per pencil = Revenue per pencil - Cost per pencil Profit per pencil = 58 - 52 Profit per pencil = [B]6[/B]

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Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B charges only $8 per kilometre travelled, but has a starting charge of $35. If Bob plans to travel 7km by bike, which rental shop should he choose for a better price [U]Shop A Cost function C(k) where k is the number of kilometers used[/U] C(k) = Cost per kilometer * k + Starting Charge C(k) = 20k With k = 7, we have: C(7) = 20 * 7 C(7) = 140 [U]Shop B Cost function C(k) where k is the number of kilometers used[/U] C(k) = Cost per kilometer * k + Starting Charge C(k) = 8k + 35 With k = 7, we have: C(7) = 8 * 7 + 35 C(7) = 56 + 35 C(7) = 91 Bog should choose [B]Shop B[/B] since they have the better price for 7km

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Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95. Since price * quantity = cost, we have the equation: 4.99b = 14.95 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=4.99b%3D14.95&pl=Solve']we type this equation into our search engine[/URL] and we get: b = [B]$3.00[/B]

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen. Let the price of each notebook be n. Let the price of each pen be p. We're given two equations: [LIST=1] [*]10n + 4p = 18 [*]6n + 4p = 12 [/LIST] Since we have matching coefficients for p, we subtract equation 1 from equation 2: (10 - 6)n + (4 - 4)p = 18 - 12 Simplifying and cancelling, we get: 4n = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4n%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 1.5[/B] Now, substitute this value for n into equation (2): 6(1.5) + 4p = 12 Multiply through: 9 + 4p = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4p%3D12&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]p = 0.75[/B]

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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]

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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]

Carrie had $32 when she got to the carnival. After riding 6 rides, she had $20 left. What was the price for each ride? If Carrie had $20 left, then the rides cost: $32 - $20 = 12 Price per ride = Cost per all rides / Total Rides Price per ride = 12/6 Price per ride = [B]2[/B]

cereal is on sale for 3.60 for a 9-ounce box. what is the price per ounce? price per ounce = Total cost / ounces price per ounce = 3.60/9 price per ounce = [B]$0.40[/B]

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cost of p pens priced at 0.29 each Cost = Price x Quantity Cost = [B]0.29p[/B]

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Dan bought a computer in a state that has a sales tax rate of 7%. If he paid $67.20 sales tax, what did the computer cost? Set up the equation for price p: p * 0.07 = 67.20 p = 67.20 / 0.07 p = [B]$960[/B]

Dawn has less than $60. She wants to buy 3 sweaters. What price of sweaters can she afford if all the sweaters are the same price? Let s be the price of each sweater. Write this as an inequality. The phrase [I]less than[/I] means an inequality, so we have the following inequality: 3s < 60 To solve this inequality, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3s%3C60&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get: s < [B]20[/B]

Deyante made a loss of $79.45 on shirt he sold for $240. What was the price of the shirt? He sold for $240. If he took a loss, that means he bought the shirt for: $240 + 79.45 = [B]$319.45[/B]

Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling x calendars income (y) = Price * Quantity [B]y = 5x[/B]

Edna plans to treat her boyfriend Curt to dinner for his birthday. The costs of their date options are listed next to each possible choice. Edna plans to allow Curt to choose whether they will eat Mexican food ($25), Chinese food ($15), or Italian food ($30). Next, they will go bowling ($20), go to the movies ($30) or go to a museum ($10). Edna also is deciding between a new wallet ($12) and a cell phone case ($20) as possible gift options for Curt. What is the maximum cost of this date? Edna has 3 phases of the date: [LIST=1] [*]Dinner [*]Event after dinner [*]Gift Option [/LIST] In order to calculate the maximum cost of the date, we take the maximum cost option of all 3 date phases: [LIST=1] [*]Dinner - Max price is Italian food at $30 [*]Event after dinner - Max price is movies at $30 [*]Gift Option - Max price option is the cell phone cast at $20 [/LIST] Add all those up, we get: $30 + $30 + $20 = [B]$80[/B]

Elli is purchasing 2.75 pounds of jelly beans which are priced at 4.85 per pound. How much change should she get back from a 20? The total bill is 4.85 per pound * 2.75 pounds = 13.34 Her change from a 20 is 20 - 13.34 = [B]6.66[/B].

Emily buys a car for 9000 sells it for 12000. Whats the profit? Profit = Sale Price - Purchase Price Profit = 12,000 - 9,000 Profit = [B]3,000[/B]

entry at a zoo costs $30 for an adult and $25 for a child. How much would it cost for 2 adults and 3 children? Cost = Price * Quantity, so we have: Cost = Price per adult * number of adults + Price per child * number of children Cost = 30 * 2 + 25 * 3 Cost = 60 + 75 Cost = [B]135[/B]

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He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is: [B]D(k) = 2k + 1.50[/B] The problem wants to know D(2.4): D(2.4) = 2(2.4) + 1.50 D(2.4) = 4.8 + 1.50 D(2.4) = [B]$6.30[/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]

How MUCH Change would be returned from a $50.00 bill for the purchase of 26 stainless Steel 8-in. bolts at the Price Of 79.5 cents each? Calculate the Stainless Steel Bolts Cost: Stainless Steel Bolts Cost = Number of Stainless Steel Bolts * Price per bolt Stainless Steel Bolts Cost = 26 * 0.795 Stainless Steel Bolts Cost = $20.67 Calculate the change: Change = Cash Offered - Stainless Steel Bolts Cost Change = $50 - $20.67 Change = [B]$29.33[/B]

How much more expensive per ounce is a 15 ounce bottle of mango juice for $3.45 than a 32 ounce bottle of mango juice for $5.12? Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=3.45&p2=5.12&q1=15&q2=32&pl=Better+Buy']better buy calculator[/URL], we get: [LIST] [*]15 oz price per ounce is $0.23 [*]32 oz price per ounce is $0.16 [*]Our answer is $0.23 - $0.16 = [B]$0.07[/B] [/LIST]

If 7 movie tickets cost $63 what is the unit price of the movie tickets? Unit Cost = Total Cost / Total Quantity Unit Cost = 63/7 Unit Cost = [B]$9 per ticket[/B]

If cats cost $15 each, what is the cost of n cats? Cost = Price x Quantity Cost = [B]15n[/B]

If I wanted to buy 40,000 balls and they are each 50 cents how much money do I need? Cost = Price * Quantity Cost = $0.50 * 40,000 Cost = [B]$20,000[/B]

If jessica buys 2 bags of chips for $3.79 each, 6 candy bars for $1.15 each, and 3 steaks for $8.45 each. How much did she pay? Calculate total cost per item, which is Price * Quantity [LIST] [*]Chips: $3.79 * 2 = $7.58 [*]Candy Bars: $1.15 * 6 = $6.90 [*]Steaks: $8.45 * 3 = $25.35 [/LIST] Total Cost = Chips Cost + Candy Bars Cost + Steaks Cost Total Cost = $7.58 + $6.90 + $25.35 Total Cost = [B]$39.83[/B]

If the cost of each hat is [I]x[/I] dollars, what is the cost of [I]y[/I] hats? Cost = Price per unit * Quantity Cost = [B]xy dollars [/B]or [B]$xy[/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 the price of cheese is $2.35 per pound, what is the cost of 2.45 pounds of cheese? Since Cost = Price * Quantity, we have: $2.35 per pound * 2.45 pounds = [B]$5.76[/B]

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how much do you pay for the entire lot of 284 bales? Since cost = price * quantity, we have: Total lot cost = price(1) of hay * bales(1) of hay + price(2) of hay * bales(2) of hay Total lot cost = 3.56 * 50 + 3.33 * 24 Total lot cost = 178 + 79.92 Total lot cost = [B]257.92[/B]

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Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90? [U]Set up the cost function C(m) where m is the number of masks:[/U] C(m) = supply cost C(m) = 50 [U]Set up the cost function R(m) where m is the number of masks:[/U] R(m) = Sale Price * m R(m) = 4m [U]Set up the profit function P(m) where m is the number of masks:[/U] P(m) = R(m) - C(m) P(m) = 4m - 50 The problems asks for profit of 90, so we set P(m) = 90: 4m - 50 = 90 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4m-50%3D90&pl=Solve']type it in our search engine[/URL] and we get: m = [B]35[/B]

Itachi want’s to buy apples that weights 5.7 pounds. The apples is priced at $1.58 per pound how much does the apples costs Cost = price per pound * number of pounds Cost = 1.58 * 5.7 Cost = [B]9.01[/B]

Jake bought s shirts. they were $7 each. Write an equation to represent the total amount that Jake paid for the shirts Since Amount = Price * Quantity, we have: [B]7s[/B]

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy. Let s be the number of sodas. Cost for the day is: Price per soda * s + Admission Price 4.25s + 42 We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55 [B]4.25s + 42 <= 55[/B] [B][/B] If the problems asks you to solve for s, we type it in our math engine and we get: Solve for [I]s[/I] in the inequality 4.25s + 42 ? 55 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 42 and 55. To do that, we subtract 42 from both sides 4.25s + 42 - 42 ? 55 - 42 [SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE] 4.25s ? 13 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE] 4.25s/4.25 ? 13/4.25 [B]s ? 3.06[/B]

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar. with a ticket price of t, we have the total cost written as: 1.04 * (7*4 + 4t)= 407.68 Divide each side by 1.04 1.04 * (7*4 + 4t)/1.04= 407.68/1.04 Cancel the 1.04 on the left side and we get: 7*4 + 4t = 392 28 + 4t = 392 To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=28%2B4t%3D392&pl=Solve']type it in our math engine[/URL] and we get: t = [B]91[/B]

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon? Price per gallon = Total spend / number of gallons Price per gallon = $46.20/12 Price per gallon = $[B]3.85[/B]

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost? Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations: [LIST=1] [*]12c + 8t = 34 <-- Jill [*]10c + 7t = 29 <-- Jack [/LIST] We have a system of equations. We can solve this one of three ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]t = 2[/B] [*][B]c = 1.5[/B] [/LIST]

Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost of one cd. [U]Let c be the cost of one CD. Set up the equation:[/U] 9c + 20 = 119 [U]Use the [URL='http://www.mathcelebrity.com/1unk.php?num=9c%2B20%3D119&pl=Solve']equation solver[/URL]:[/U] [B]c = 11[/B]

John bought a painting for $600 and sold it for $648. Find the profit as a percentage of the cost. [U]Calculate the profit:[/U] Profit = Sale Price - Purchase price Profit = 648 - 600 Profit = 48 [U]Calculate Profit percentage of cost =[/U] Profit percentage of cost = 100% * Profit/cost Profit percentage of cost = 100% * 48 / 600 Profit percentage of cost = [B]8%[/B]

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD? Let the price of each cd be c. We're given the equation: 9c + 9.45 = 118.89 [URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get: c = [B]12.16[/B]

Karen bought a bucket of popcorn at the movies for $5. She also bought some candy for $2 each. Karen has to spend less than $15 on the popcorn and candy. Which inequality can be used to find c, the number of candies that Karen could have bought? Since the candy cost is the product of price and quantity, we have: 2c + 5 < 15 To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B5%3C15&pl=Solve']type it in our math engine [/URL]and we get: [B]c < 5[/B]

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges [U]Assumptions and givens:[/U] [LIST] [*]Let a be the total cost of apples [*]Let o be the total cost of oranges [/LIST] The phrase [I]at most[/I] means less than or equal to, so we have: a + o <= 2.50 [U]Find the cost of apples (a)[/U] a = price per apple * quantity of apples a = 0.36 * 5 a = 1.8 Our new inequality with a = 1.8 is: 1.8 + o <= 2.50 [URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get: [B]o <= 0.7[/B]

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet and each table top has a diameter of 4 feet. If the price of a piece of plywood is $40, what is the value of the plywood that is wasted after the table tops are cut? Area of the plywood = 4 * 8 = 32 square feet [U]Calculate area of 1 round top[/U] Diameter = 2 Radius = Diameter/2 = 4/2 = 2 Area of each round top = pir^2 Area of each round top = 3.14 * 2 * 2 Area of each round top = 12.56 square feet [U]Calculate area of 2 round tops[/U] Area of 2 round tops = 12.56 + 12.56 Area of 2 round tops = 25.12 sq feet [U]Calculate wasted area:[/U] Wasted area = area of the plywood - area of 2 round tops Wasted area = 32 - 25.12 Wasted area = 6.88 sq feet [U]Calculate cost per square foot of plywood:[/U] Cost per sq foot of plywood = Price per plywood / area of the plywood Cost per sq foot of plywood = 40/32 Cost per sq foot of plywood = $1.25 [U]Calculate the value of the plywood:[/U] Value of the plywood = Wasted Area sq foot * Cost per sq foot of plywood Value of the plywood = 6.88 * 1.25 Value of the plywood = [B]$8.60[/B]

Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muffin costs $0.75. What’s an equation? Let m be the number of muffins. Cost equals price * quantity, so we have: [B]0.75m = 5.25 [/B] To solve the equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75m%3D5.25&pl=Solve']type the equation into our search engine[/URL] and we get: m = [B]7[/B]

kim wants to buy candy for 4 dollars a pound. if she wants to spend less than 20 dollars, how many bags can she buy Since cost = price * quantity, we have the following inequality with b as the number of bags: 4b < 20 To solve this inequality for b, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4b%3C20&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get: [B]b < 5[/B]

Lamar had N record albums that he tried to sell at a garage sale for $5 each. If the number of record albums he didn't sell is called Q, how much money did Lamar get from record album sales? Sales = Price * (Albums had - Albums sold) [B]Sales = 5(N - Q)[/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]

Luna had $50 when she got to the carnival. After riding 12 rides she had $26. What was the price after each ride? After riding 12 rides, Lucy had $26. Which means she spent $50 - $26 = $24. $24 / 12 rides = [B]$2 per ride[/B].

Marina bought 4 notebooks, which cost b dollars each and 3 pens, which cost c dollars each. How much money did Marina spend? Cost = Quantity * Price, so we have total spend S of: S = [B]4b + 3c[/B]

Free Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Martin buys b books at £10 each what is the total cost Total Cost = Price * Quantity Total Cost = £10 * b Total Cost = [B]£10b[/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]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box. [U]Calculate total sales:[/U] Total Sales = Number of Books * Price per book Total Sales = 50,000 * $35 Total Sales = $1,750,000 [U]Now calculate Mike's royalties:[/U] Royalties = Total Sales * Royalty Percent Royalties = $1,750,000 * 15% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/B]

Mr rosenthal bought 15 computer disks and a carrying case for 28.50 if the carrying case cost 6.75 what was the cost of each disk Figure out how much he has left over after purchasing the carrying case: 28.50 - 6.75 = 21.75 Now, figure out the price per disk: 21.75/15 = [B]1.45[/B]

Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake Let the cost for work be w. Let the cost for each tire be t. We're given; [LIST=1] [*]w = 5t [*]w + 4t = 1035 [/LIST] Substitute equation 1 into equation 2: (5t) + 4t = 1035 [URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get: t = 115 Substitute this into equation (1): w = 5(115) w = [B]575[/B] The mechanic underestimated the work cost.

On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel Let the number of cups of coffee be c Let the number of bagels be b. Since cost = Price * Quantity, we're given two equations: [LIST=1] [*]7b + 4c = 8.77 [*]14b + 8c = 15.80 [/LIST] We have a system of equations. We can solve this 3 ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer [LIST] [*]The system is inconsistent. Therefore, we have no answer. [/LIST]

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket? Let the number of child tickets be c Let the number of senior citizen tickets be s We're given two equations: [LIST=1] [*]10c + 3s = 82 [*]5c + 8s = 67 [/LIST] We have a system of simultaneous equations. We can solve it using any one of 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]

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Free Percentage of Completion Calculator - Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Pound of strawberries for $4.00. What is the price, in dollars, per ounce of strawberries? 1 pound equals 16 ounces. So the pounds per ounce equals: $4.00/16 ounces Divide top and bottom by 16, we get: [B]$0.25 per ounce[/B]

Free Price Calculator - Given a cost and a gross margin percentage, this calculator calculates price, gross profit, markup percentage

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun. We want a sales function p where c is the number of copies of Math is Fun p = Price per sale * c + Base Salary [B]p = 40c + 1900 [/B] Now, we want to know Total pay if c = 22 p = 40(22) + 1900 p = 880 + 1900 p = [B]2780[/B]

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Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent. Let d be the cost of each drink, and p be the price of each popcorn bag. We have 2 equations for our system of equations: [LIST=1] [*][B]4d + 9p = 65.25[/B] [*][B]8d + 3p = 51.75[/B] [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+9p+%3D+65.25&term2=8d+%2B+3p+%3D+51.75&pl=Cramers+Method']system of equations calculator[/URL], we get: [LIST] [*]d = 4.5 [*][B]p = 5.25 <-- Since the problem asks for the cost of each popcorn bag[/B] [/LIST]

Let x be the price of one t-shirt. Set up an equation: 6 times the number of t-shirts plus 7 dollars left over get him to a total of 45 6x = 45 - 7 6x = 38 Divide each side by 6 [B]x = 6.33[/B]

Ryan buys candy that costs $4 per pound. He will buy at least 12 pounds of candy. What are the possible amounts he will spend on candy? Clue for you: the phrase [I]at least[/I] means an inequality. Let s be the spend on candy. Cost = Price * quantity Cost = 4 * 12 Cost = 48 The phrase [I]at least[/I] means greater than or equal to: [B]s >= 48[/B]

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Free Sales Tax Calculator - Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an item that costs d dollars after tax is added to the purchase. We need to increase the price by 9.1%. Our expression is: [B]1.091d[/B]

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is the sales tax on a $9000 automobile? Set up a proportion of sales tax to purchase price where s is the sales tax on a 9000 automobile: 240/46000 = s/9000 [URL='https://www.mathcelebrity.com/prop.php?num1=240&num2=s&den1=46000&den2=9000&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL] and we get: s = [B]46.96[/B]

Sam had 120 teddy bears in his toy store. He sold 2/3 of them at $12 each. How much did he receive? Revenue = Price * Quantity 12 * 2/3 * 120 12 * 80 [B]960[/B]

She bought 120 sodas for $1.25 each, 30 pizzas for $12.50 each and 120 packs of skittles for $2 each. Total Cost = Soda Cost + Pizza Cost + Skittle Cost Cost = Quantity * Price, so we have: Total Cost = 120 * 1.25 + 20 * 12.50 + 120 * 2 Total Cost = 150 + 250 + 240 Total Cost = $[B]640[/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]

Shen buys a pack of 9 towels for $24.30. Find the unit price in dollars per towel. Unit Price = Total Price/Units Unit Price = 24.30/9 Unit Price = [B]2.7[/B]

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]18.09[/B]

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket? Let the number of adult tickets be a Let the number of student tickets be s We're given two equations: [LIST=1] [*]30a + 30s = 750 [*]27a + 28s = 682 [/LIST] To solve the simultaneous equations, we can use any of three methods below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get the same answers: [LIST] [*][B]a = 18[/B] [*][B]s = 7[/B] [/LIST]

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295 Set up the cost function C(p) where p is the number of purses: C(p) = Cost per purse * p + Booth Rental C(p) = 15p + 50 Set up the revenue function R(p) where p is the number of purses: R(p) = Sale price * p R(p) = 30p Set up the profit function which is R(p) - C(p) equal to 295 30p - (15p + 50) = 295 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get: p = [B]23[/B]

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3 of the avagrage price at a consignment shop. How much money did she make at the consigment shop? Calculate average price: 1/3 the average price is $30/3 = $10 Total money made: Pairs of Shoes * Average Price 15 * 10 = [B]$150[/B]

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the cost of 12 notebooks at x pesos each Cost = quantity * price Cost = [B]12x[/B]

The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the possible prices of one apple? Let a be the price of each apple. We're given 2 inequalities: [LIST=1] [*]25a < 9.50 [*]12a > 3.60 [/LIST] [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=25a%3C9.50&pl=Show+Interval+Notation']Typing 25a < 9.50 into our search engine[/URL], we get a < 0.38 [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12a%3E3.60&pl=Show+Interval+Notation']Typing 12a > 360 into our search engine[/URL], we get a > 0.3 Therefore, the possible prices a of one apple are expressed as the inequality: [B]0.3 < a < 0.38[/B]

the cost of 3 notebooks at m dollars each Cost = Quantity x Price Cost = [B]3m[/B]

the cost of 7 CD at d$ each The cost is price * quantity [B]7d[/B]

the cost of b books at p dollars each Cost = Price * Quantity, so we have: Cost = [B]pb[/B]

the cost of d drinks at $2 each and 5 pies at $n each Total cost = Price * Quantity: Total cost = [B]2d + 5n[/B]

The cost of x movies if each movie cost $20 Cost = Price * Quantity, so we have: Cost = [B]20x[/B]

The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/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 PLAYER CHOSE 20 OUT OF 70 NUMBERS IN A GAME OF CHANCE. ...WHEN THE SHOW BEGIN,THE BANKER WILL THEN RAFFLE OR DO A DRAW WHERE IN THE BANKER PICKS AS WELL 20 OUT OF 70 NUMBERS. .....NOW HERES THE TRICK, FOR YOU TO BEAT THE BANKER .YOUR CHOSEN 20 NUMBERS SHOULD NOT MATCH ANY OF THE BANKER 20 0UT OF 70 NUMBERS THAT HAD BEEN DRAWS IN THE GAME OF SHOW. IF THE 20 NUMBERS YOU HAVE ARE TOTALLY DIFFERENT FROM THE BANKERS 20 NUMBERS DRAWN THEN YOU WIN THE PRICE. Banker Draw Numbers not matching Total numbers Probability Probability Decimal Cumulative Probability 1 50 70 50/70 0.7142857143 0.7142857143 2 49 69 49/69 0.7101449275 0.5072463768 3 48 68 48/68 0.7058823529 0.358056266 4 47 67 47/67 0.7014925373 0.2511737985 5 46 66 46/66 0.696969697 0.1750605262 6 45 65 45/65 0.6923076923 0.1211957489 7 44 64 44/64 0.6875 0.0833220774 8 43 63 43/63 0.6825396825 0.05687062425 9 42 62 42/62 0.6774193548 0.03852526159 10 41 61 41/61 0.6721311475 0.02589402828 11 40 60 40/60 0.6666666667 0.01726268552 12 39 59 39/59 0.6610169492 0.01141092772 13 38 58 38/58 0.6551724138 0.007476125057 14 37 57 37/57 0.649122807 0.004852923282 15 36 56 36/56 0.6428571429 0.003119736396 16 35 55 35/55 0.6363636364 0.001985286797 17 34 54 34/54 0.6296296296 0.001249995391 18 33 53 33/53 0.6226415094 0.000778299017 19 32 52 32/52 0.6153846154 0.0004789532412 20 31 51 31/51 0.6078431373 [B]0.0002911284407 [/B]

The price of a baseball glove is no more than $38.95. Let p be the price of the baseball glove. The phrase "no more than" means less than or equal to. Our inequality is: p <= $38.95

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack? backpack cost = b Cheap backpack = b - 15 The total of both items equals 75: b + b - 15 = 75 Solve for [I]b[/I] in the equation b + b - 15 = 75 [SIZE=5][B]Step 1: Group the b terms on the left hand side:[/B][/SIZE] (1 + 1)b = 2b [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2b - 15 = + 75 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -15 and 75. To do that, we add 15 to both sides 2b - 15 + 15 = 75 + 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] 2b = 90 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2b/2 = 90/2 b = 45 Cheap backpack = 45 - 15 = [B]30 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb-15%3D75&pl=Solve']Source[/URL][/B]

The price of a gallon of gasoline is $3.15. The price when Ryan’s mother started driving was 1/7 of the current price. What was the price of gasoline when Ryan’s mother started driving? $3.15/7 = [B]$0.45[/B]

the price of a remote control helicopter is $34.40. a remote control boat costs 4/5 the price of the helicopter. sales tax on the remote control boat is 8%.what is the price of the remote control boat, including sales tax? round your answer to the nearest penny 4/5 of 34.40 = $27.52 Add sales tax: 27.52(1.08) = [B]$29.72[/B]

The price p of a gym’s membership is $30 for an enrollment fee and $12 per week w to be a member. What is the cost to be a member for 5 weeks? Set up the cost function C(w) C(w) = 12w + 30 The problem asks for C(5) C(5) = 12(5) + 30 C(5) = 60 + 30 C(5) = [B]90[/B]

the price p per gallon g Price per gallon = Price / Gallons Price per gallon = [B]p/g[/B]

The property taxes on a boat were $375. What was the tax rate if the boat was valued at $75,000? Tax Rate = Tax Amount / Purchase Price Tax Rate = 375 / 75,000 Tax Rate = 0.005 Tax Rates are generally expressed in percentages, so the percentage = 0.005 * 100 = [B]0.5%[/B].

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket? Let the cost of child tickets be c Let the cost of senior tickets be s Since revenue = cost * quantity, we're given two equations: [LIST=1] [*]9c + 3s = 75 [*]5c + 8s = 67 [/LIST] To solve this simultaneous group of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]

The regular cost of a guitar is n. On Saturdays, all guitars are 15% off. What is the price of the guitar on Saturday? 15% = 0.15 If we take that price off, we have: 1 - 0.15 = 0.85 So the cost is [B]0.85n[/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 sales price s of a pair of shoes plus 4% sales tax Total price is s(1 + 0.04) or [B]s(1.04)[/B]

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones at $47.44 each? What is the total price? [U]First, calculate the pre-tax price:[/U] Pre-tax price = Price per headphone * Number of Headphones Pre-tax price = $47.44 * 5 Pre-tax price = $237.20 Now calculate the tax amount: Tax Amount = Pre-Tax Price * (Tax Rate / 100) Tax Amount = $237.20 * 7.27/100 Tax Amount = $237.20 * 0.0727 Tax Amount = [B]$17.24 [/B] Calculate the total price: Total Price = Pre-Tax price + Tax Amount Total Price = $237.20 + $17.24 Total Price = [B]$254.44[/B]

The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant. Let the cost of each fern be f Let the cost of each ivy plant be I We're given: [LIST=1] [*]12f + 8i = 260 [*]15i + 6f = 240 [/LIST] To solve this system of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]f = 7.5[/B] [*][B]i= 21.25[/B] [/LIST]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point. [U]Calculate cost function C(b) with b as the number of books:[/U] C(b) = Cost per book * b + Overhead [B]C(b) = 15b + 5500[/B] [U]Calculate Revenue Function R(b) with b as the number of books:[/U] R(b) = Sales Price per book * b [B]R(b) = 40b[/B] [U]Calculate break even function E(b):[/U] Break-even Point = Revenue - Cost Break-even Point = R(b) - C(b) Break-even Point = 40b - 15b - 5500 Break-even Point = 25b - 5500 [U]Calculate break even point:[/U] Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0 25b - 5500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: [B]b = 220[/B]

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the price of a single dress using the cost-plus method will be The phrase [I]unit cost[/I] means price per one unit. [U]Unit cost for one dress is:[/U] Price of dresses / Number of dresses 1500/100 15 Each dress cost $15 which is the unit cost [U]Cost plus method:[/U] Cost plus price = Unit price + Unit price * markup Cost plus price = 15 + 15 * 20% Cost plus price = 15 + 3 Cost plus price = [B]$18 [MEDIA=youtube]H9rOp592y5s[/MEDIA][/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]

Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1340 tickets sold for a total of $12,200. How many student tickets were sold? Let s be the number of student tickets and n be the number of nonstudent tickets: [LIST=1] [*]n + s = 1340 [*]10n + 8s = 12200 [/LIST] Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+s+%3D+1340&term2=10n+%2B+8s+%3D+12200&pl=Cramers+Method']simultaneous equation calculator[/URL]: n = 740 [B]s = 600[/B]

Tickets to the amusement park cost $12 for adults and $8 for kids. Write on algebraic expression to show the cost of a adult and k kids Since cost = price * quantity, we have: [B]12a + 8k[/B]

Todd bought 5 ice cream sandwiches for $3.75. Bryce bought one ice cream sandwich for $1.00. Who got the better deal? Todd's unit cost is found by: Todd's Unit Cost = Total Price / Total Ice Cream Sandwiches Todd's Unit Cost = $3.75/5 Todd's Unit Cost = $0.75 Bryce's unit cost is $1.00 per ice cream sandwich, so [B]Todd got the better deal.[/B]

Tom has t dollars. He buys 5 packets of gum worth d dollars each. How much money does he have left Since cost = Price * Quantity, and a purchase reduces Tom's money, we have: [B]t - 5d[/B]

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Wayne’s widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks them up $6.79. What is the retail price at this store? [I]Note: Markup means we add to the wholesale price. [/I] Calculate Retail Price: Retail Price = Wholesale Price + Markup Amount Retail Price = $10.20 + $6.79 Retail Price = [B]$16.99[/B]

what is the cost of 3 books at p cents and 4 pens at q cents each? Cost = Price * Quantity. [B]3p + 4q[/B]

x textbooks if one textbook costs $140 Since cost = price * quantity, we have: Total cost = Cost per textbook * number of text books Total cost = [B]140x[/B]

Yasmine bought 3 candy bars at a cost of $0.85 each and 2 bags of peanuts at $1.25 each. Cost = Price * Quantity, so we have: Cost = 3 * 0.85 + 2 * 1.25 Cost = 2.55 + 2.50 Cost = [B]$4.55[/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]

You and some friends are going to the fair. Each ticket for a ride costs $0.75. If n is the number of tickets purchased, write an expression that gives the total cost of buying n tickets. We know cost = Price * Quantity, so we have: Cost of buying n tickets = [B]0.75n[/B]

You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal? Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A. [U]Company B conversion:[/U] Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion: $19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot. Now, let's set up the cost equations C(s) for each Company in square feet (s) [LIST] [*]Company A: C(s) = 200 + 2.99s [*]Company B: C(s) = 500 + 2.22s [/LIST] The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500) [U]Company A:[/U] C(1500) = 200 + 2.99(1500) C(1500) = 200 + 4485 C(1500) = 4685 [U]Company B:[/U] C(1500) = 500 + 2.22(1500) C(1500) = 500 + 3330 C(1500) = 3830 Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.

You are researching the price of DVD players. You found an average price of $58.80. One DVD player costs $56 and another costs $62. Find the price of the third DVD player. We want to find n, such that n makes the average of the 3 DVD players $58.80. [URL='https://www.mathcelebrity.com/missingaverage.php?num=56%2C62&avg=58.80&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], we get the price of the 3rd DVD player is $58.40.

You buy 4 magazines for $5 each and 2 drinks for $4 each Calculate total cost: Since cost = price * quantity, we have: Total cost = $5 * 4 magazines + $4 * 2 drinks Total cost = 20 + 8 Total Cost = [B]28[/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 can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket We're given the number of tickets as 5. We know cost = price * quantity Let p = price The phrase [B]at most[/B] means less than or equal to, so we have: 5p <= 35 [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=5p%3C%3D35&pl=Show+Interval+Notation']Plugging this inequality into our search engine[/URL], we have: [B]p <= 7[/B]

You have $10.00 to spend on tacos. Each taco costs $0.50. Write and solve an inequality that explains how many tacos you can buy. Let's start with t as the number of tacos. We know that cost = price * quantity, so we have the following inequality for our taco spend: [B]0.5t <= 10 [/B] Divide each side of the inequality by 0.5 to isolate t: 0.5t/0.5 <= 10/0.5 Cancel the 0.5 on the left side and we get: t <= [B]20 [MEDIA=youtube]yy51EsGi1nM[/MEDIA][/B]

You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which equation represents the relation between the number of cotton candy (c) and soda pops (s) you can buy? Our total cost for 20 at the state fair is: Cost of Cotton Candy + Cost of Soda = 20 We know that price = cost * quantity, so we have: 2c + 1s = 20 Since 1s is written as s, we have: [B]2c + s = 20[/B]

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