Let Carlos's age be a. Twice a means we multiply by 2 2a 70 decreased by that amount means we subtract: [B]70 - 2a[/B]

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400? Let the amount of consecutive hits needed be h. We have: hits / at bats = Batting Average Plugging in our numbers, we get: (9 + h)/60 = 0.400 Cross multiply: 9 + h = 60 * 0.4 9 + h = 24 To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get: h = [B]15[/B]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: [LIST=1] [*]a + b = 44 [*]10a + 20b = 730 [/LIST] We rearrange equation 1 in terms of a. We subtract b from each side and we get: [LIST=1] [*]a = 44 - b [*]10a + 20b = 730 [/LIST] Now we substitute equation (1) for a into equation (2): 10(44 - b) + 20b = 730 Multiply through to remove the parentheses: 440 - 10b + 20b = 730 Group like terms: 440 + 10b = 730 Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]29 [/B] To get a, we take b = 29 and substitute it into equation (1) above: a = 44 - 29 a = [B]15 [/B] So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be? Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations: [LIST=1] [*]f = 10s [*]s + f = 8 & 1/4 [/LIST] Substitute (1) into (2): s + 10s = 8 & 1/4 11fs= 33/4 <-- 8 & 1/4 = 33/4 Cross multiply: 44s = 33 Divide each side by 44: s= 33/44 Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B] Now substitute this into (1): f = 10(33/44) [B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours? Assumptions and givens; [LIST] [*]h is the number of hours. [*]B(h) is the number of bacteria at time h [*]B(0) is the starting bacteria amount [*]Doubling means multiplying by 2, so we have: [/LIST] B(h) = B(0) * 2^h We want h = 9, so we have: B(9) = 500 * 2^9 B(9) = 500 * 512 B(9) = [B]256,000[/B]

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exist after 3 days? Determine the amount of tripling periods: [LIST] [*]There are 24 hours in a day. [*]24 hours in a day * 3 days = 72 hours [*]72 hours / 6 hours tripling period = 12 tripling periods [/LIST] Our bacteria population function B(t) where t is the amount of tripling periods. Tripling means we multiply by 3, so we have: B(t) = 2000 * 3^t with t = 12 tripling periods, we have: B(12) = 2000 * 3^12 B(12) = 2000 * 531441 B(12) = [B]1,062,882,000[/B]

a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are needed for 30 bread rolls? Set up a proportion of bread rolls per tablespoons of butter where t is the amount of tablespoons of butter needed for 30 bread rolls: 20/5 = 30/t Cross multiply our proportion: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 20t = 30 * 5 20t = 150 Divide each side of the equation by 20: 20t/20 = 150/20 Cancel the 20's on the left side and we get: t = [B]7.5[/B]

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions? We know the rectangle has the following formulas: Area = lw Perimeter = 2l + 2w Given an area of 238 and a perimeter of 62, we have: [LIST=1] [*]lw = 238 [*]2(l + w) = 62 [/LIST] Divide each side of (1) by w: l = 238/w Substitute this into (2): 2(238/w + w) = 62 Divide each side by 2: 238/w + w = 31 Multiply each side by w: 238w/w + w^2 = 31w Simplify: 238 + w^2 = 31w Subtract 31w from each side: w^2 - 31w + 238 = 0 We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get: w = (14, 17) We take the lower amount as our width and the higher amount as our length: [B]w = 14 l = 17 [/B] Check our work for Area: 14(17) = 238 <-- Check Check our work for Perimeter: 2(17 + 14) ? 62 2(31) ? 62 62 = 62 <-- Check

A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax. Calculate the tip: Tip = Bill Before Tax * Tip % Tip = $28.35 * 20% Tip = $5.67 Calculate Tax: Tax = Bill without Tip * Tax % Tax = $28.35 * 6.25% Tax = $1.77 Total Cost = Bill + Tax + Tip Total Cost = $28.35 + $5.67 + $1.77 Total Cost = [B]$35.79[/B]

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have: (1073 + 1108 + s)/3 = 1000 Cross multiply: 1073 + 1108 + s = 1000 * 3 1073 + 1108 + s = 3000 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]819[/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 spherical water tank holds 11,500ft^3 of water. What is the diameter? The tank holding amount is volume. And the volume of a sphere is: V = (4pir^3)/3 We know that radius is 1/2 of diameter: r =d/2 So we rewrite our volume function: V = 4/3(pi(d/2)^3) We're given V = 11,500 so we have: 4/3(pi(d/2)^3) = 11500 Multiply each side by 3/4 4/3(3/4)(pi(d/2)^3) = 11,500*3/4 Simplify: pi(d/2)^3 = 8625 Since pi = 3.1415926359, we divide each side by pi: (d/2)^3 = 8625/3.1415926359 (d/2)^3 = 2745.42 Take the cube root of each side: d/2 = 14.0224 Multiply through by 2: [B]d = 28.005[/B]

A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and spends $60, how many of each did he buy? Let the amount of small notebooks be s. Let the amount of large notebooks be l. We're given two equations: [LIST=1] [*]l + s = 6 [*]12l + 6s = 60 [/LIST] Multiply equation (1) by -6 [LIST=1] [*]-6l - 6s = -36 [*]12l + 6s = 60 [/LIST] Now add equation 1 to equation 2: 12l - 6l + 6s - 6s = 60 - 36 Cancel the 6s terms, and we get: 6l = 24 To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l%3D24&pl=Solve']type this equation into our search engine[/URL] and we get: l = [B]4 [/B] Now substitute this into equation 1: 4 + s = 6 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=4%2Bs%3D6&pl=Solve']we type this equation into our search engine[/URL] and we get: s = [B]2[/B]

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the total did he spend on fruit? 51/60 = 0.85 Multiply 0.85 by 100 to get the percentage 0.85 * 100 = [B]85%[/B]

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

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

At what simple interest rate will 4500$ amount to 8000$ in 5 years? Simple Interest is written as 1 + it. With t = 5, we have: 4500(1 + 5i) = 8000 Divide each side by 4500 1 + 5i = 1.77777778 Subtract 1 from each side: 5i = 0.77777778 Divide each side by 5 i = 0.15555 As a percentage we multiply by 100 to get [B]15.5%[/B]

If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 4 don't grow? Im seriously confused is it like u multiple the amount of the (0.90) and multiple (0.30) by power depends how any they r right?

Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with? Let the starting amount of cards be s. We're given: [LIST] [*]Dan bought 7 new cards: s + 7 [*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2 [*]Now, he's got 26 cards left. So we set up the following equation: [/LIST] (s + 7)/2 = 26 Cross multiply: s + 7 = 26 * 2 s + 7 = 52 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get: s = [B]45[/B]

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left over, how much did each person eat? This means 4 full pizzas - 1/4 of a pizza = 3 & 3/4 pizzas eaten Del and his 5 friends means 6 people total. Since they ate equal amounts, we divide pizzas eaten by total people: 3 & 3/4 / 6 Convert 3 & 3/4 to a mixed fraction: (4*3 + 3)/4 = 15/4 15/4/6 Divide by a fraction is the same as multiply by a reciprocal: 15/4 * 1/6 = [B]15/24 pizzas per person[/B]

Estimate a 15% tip on a dinner bell of $49.76 by first round the bill amount to the nearest $10. Round the bill to the nearest $10 [LIST] [*]$49.76 is in between ($40, $50) [*]1/2 of that interval is (40 + 50)/2 = 90/2 = 45 [*]Since $49.76 is greater than or equal to 45, we round up to $50 [/LIST] Add a 15% tip 50(1 + 0.15) = 50 + 7.50 = [B]$57.50[/B]

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.) a. Create an equation from the information above. b. Identify the slope in the equation? c. Calculate the total cost of the ride? 2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you a. Cost Equation C(m) for m miles is as follows: [B]C(m) = 1.57m + 5 [/B] b. Slope of the equation is the coefficient for m, which is [B]1.57 [/B] c. Total cost of the ride for m = 12 miles is: C(12) = 1.57(12) + 5 C(12) = 18.84 + 5 C(12) = [B]23.84 [/B] d. If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount: 50 - 7.50 = 42.50 So C(m) = 42.50 1.57m + 5 = 42.50 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.57m%2B5%3D42.50&pl=Solve']type it in our search engine[/URL] and we get: m = 23.89 Since we deal in full miles, we round our answer down to m = [B]23[/B]

Lisa has 32 nickels this is one third of her coins how many coins does she have Let x be the total amount of coins. we have: 32 = x/3 Cross multiply, we get: [B]x = 96[/B]

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

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Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work? [LIST] [*]Let [I]s[/I] be the number of hours Sally works every week. [*]Let [I]a[/I] be the number of hours Adam works every week. [*]We are given: a = s + 2 [/LIST] Sally's weekly earnings: 5s Adam's weekly earnings: 4a Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings: 5s = 4a But remember, we're given a = s + 2, so we substitute this into Adam's earnings: 5s = 4(s + 2) Multiply through on the right side: 5s = 4s + 8 <-- [URL='https://www.mathcelebrity.com/expand.php?term1=4%28s%2B2%29&pl=Expand']multiplying 4(s + 2)[/URL] [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D4s%2B8&pl=Solve']Typing this equation into the search engine[/URL], we get s = 8. The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours: a = s + 2 a = 8 + 2 [B]a = 10[/B]

Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with. Let the amount Steven started with be s. We're given: s - 9 = 3s/5 Multiply each side through by 5 to eliminate the fraction: 5(s - 9) = 5(3s/5) Cancel the 5's on the right side and we get: 5s - 45 = 3s To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]22.5[/B]

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Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start? Let the starting candy amount be c. We're given: (c - 5)/3 = 3 Cross multiply: c - 5 = 3*3 c - 5 = 9 [URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get: c = 14

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you work? To figure out the hours worked, we first need the amount of hourly wages made: Hourly Wages = Total Wages - Tips Hourly Wages = $167 - $35 Hourly Wages = $132 Calculate Hours Worked Hours Worked = Hourly Wages / Hourly Rate Hourly Worked = $132 / $8 Hourly Worked = [B]16.5[/B]

You go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%. You are planning on giving a tip on that total amount (bill and tax together) of 20%. What is your final bill, all taxes and tips included? [U]Calculate the after tax amount:[/U] After tax amount = Bill * (1 + Tax Rate) Since 9% = 0.09, we have: After tax amount = 74.26 * (1 + 0.09) After tax amount = 74.26 * 1.09 After tax amount = 80.94 [U]Calculate the Tip amount:[/U] Tip amount = After tax amount * tip percent Since 20% = 0.2, we have: Tip amount = 80.94 * 0.20 Tip amount = 16.19 [U]Calculate the final bill:[/U] Final Bill = After Tax Amount + Tip Amount Final Bill = 80.94 + 16.19 Final Bill = [B]97.13[/B]

Your bill for dinner, including a 7.25% sales tax, was $49.95. You want to leave a 15% tip on the cost of the dinner before the sales tax. Find the amount of the tip to the nearest dollar. Find the pretax cost: 49.95/1.0725 = 46.57 Now, add 15% tip to the pretax bill: 46.57(1.15) = [B]$53.56[/B]