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3. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow the same lawn with a push mower in 4 hours. How long will it take to mow the lawn if they work together?

3. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow the same lawn with a push mower in 4 hours. How long will it take to mow the lawn if they work together?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For #43, I'm not sure where the 1/n came from or how 3/4 became 4/3.

12:15 AM Wed Mar 16 70% AA A bartleby.com Secondary Pro... Free Chart - A... - www.astro.co... b The time requi... * Favorites Q SEARCH & ASK AN EXPERT CHAT Vx MATH SOLVER Expert Solution & Answer Answer to Problem 43E They will take 1- hours to mow a lawn working together. Explanation of Solution Given: Time required by Julie = 2 hours Time required by Husband = 4 hours Approach: As Julie can mow a lawn in 2 hours, the part of work she can do in one hour =. As Julie's husband can mow a lawn in 4 hours, the part of work he can do in one hour =. Now let's assume they can mow a lawn in 'n' hours working together. Then the part of work they can do in one hour =-. n Calculation: We have, : = + 1 n 2 Solve this equation for n, 1 2 + 1 [LCM of (2, 4) = 4] 4 n 1 3 n 4 4 n = 3 3 Final Statement: They will take 1, hours to mow a lawn working together. < Previous Next > Chapter 1.2, Problem 42E Chapter 1.2, Problem 44E Got some follow up questions? Date this solutien
Transcribed Image Text:12:15 AM Wed Mar 16 70% AA A bartleby.com Secondary Pro... Free Chart - A... - www.astro.co... b The time requi... * Favorites Q SEARCH & ASK AN EXPERT CHAT Vx MATH SOLVER Expert Solution & Answer Answer to Problem 43E They will take 1- hours to mow a lawn working together. Explanation of Solution Given: Time required by Julie = 2 hours Time required by Husband = 4 hours Approach: As Julie can mow a lawn in 2 hours, the part of work she can do in one hour =. As Julie's husband can mow a lawn in 4 hours, the part of work he can do in one hour =. Now let's assume they can mow a lawn in 'n' hours working together. Then the part of work they can do in one hour =-. n Calculation: We have, : = + 1 n 2 Solve this equation for n, 1 2 + 1 [LCM of (2, 4) = 4] 4 n 1 3 n 4 4 n = 3 3 Final Statement: They will take 1, hours to mow a lawn working together. < Previous Next > Chapter 1.2, Problem 42E Chapter 1.2, Problem 44E Got some follow up questions? Date this solutien
Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 106 Chapter 1 Equations and Inequalities 25. Investment Jeffrey invested $16,000 in two accounts paying 4% and 6% annual interest. If the total interest earned in one year was $815, how much did XXO he invest at each rate? 26. Investment An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1420, how much is invested at XXO each rate? 27. Financial planning After inheriting some money, a woman wants to invest enough to have an annual income of $5000. If she can invest $20,000 at 9% annual interest, how much more will she have to invest at 7% to achieve her goal? (See the table.) 36. Markup A merchant increases the wholesale cost of a surfboard by 30% to determine the selling price. If the surfboard sells for $588.90, find the wholesale cost. 37. Break-point analysis A machine to mill a brass plate has a setup cost of $600 and a unit cost of $3 for each plate manufactured. A bigger machine has a setup cost of $800 but a unit cost of only $2 for each plate manufactured. Find the break point. Туре Rate Amount Income 9% investment 0.09 20,000 .09(20,000) 7% investment 0.07 .07x 28. Investment A woman invests $37,000, part at 8% and the rest at 9% annual interest. If the 95% investment provides $452.50 more income than the 8% investment, how much is invested at each rate? 38. Break-point analysis A machine to manufacture fasteners has a setup cost of $1200 and a unit cost of $0.005 for each fastener manufactured. A newer machine has a setup cost of $1500 but a unit cost of only $0.0015 for each fastener manufactured. Find the break point. 29. Investment Equal amounts are invested at 6%, 7%, and 8% annual interest. If the three investments 39. Computer sales A computer store has fixed costs of $8925 per month and a unit cost of $850 for every computer it sells. If the store can sell all the comput- ers it can get for $1275 each, how many must be sold for the store to break even? (Hint: The break-even point occurs when costs equal income.) yield a total of $2037 annual interest, find the total investment. 30. Investment Aaron invested equal amounts of money at 5%, 7%, 9%, and 11% annual interest. If the four investments yielded a total of $1440 annual interest, find the total amount 40. Restaurant management A restaurant has fixed costs of $137.50 per day and an average unit cost of $4.75 for each meal served. If a typical meal costs $6, how many customers must eat at the restaurant each day for the owner to break even? invested. 31. Ticket sales A full-price ticket for a college bas- ketball game costs $2.50, and a student ticket costs $1.75. If 585 tickets were sold, and the total receipts were $1,217.25, how many tickets were student tickets? 32. Ticket sales Of the 800 tickets sold to a movie, 480 were full-price tickets costing $7 each. If the gate receipts were $4960, what did a student ticket cost? 41. Roofing houses Kyle estimates that it will take him 7 days to roof his house. A professional roofer estimates that it will take him 4 days to roof the same house. How long will it take if they work together? 33. Discount An iPad Air is on sale for $413.08. What was the original price of the iPad if it was dis- counted 8%? 42. Sealing asphalt One crew can seal a parking lot in 8 hours and another in 10 hours. How long will it take to seal the parking lot if the two crews work together? 34. Discount After being discounted 20%, a weather radio sells for $63.96. Find the original price. 35. Markup A business owner increases the wholesale cost of a kayak by 70% and sells it for $365.50. Find the wholesale cost. 43. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow the same lawn with a push mower in 4 hours. How long will it take to mow the lawn if they work together? Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. ©Kalmatsuy/Shutterstock.com
Transcribed Image Text:Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 106 Chapter 1 Equations and Inequalities 25. Investment Jeffrey invested $16,000 in two accounts paying 4% and 6% annual interest. If the total interest earned in one year was $815, how much did XXO he invest at each rate? 26. Investment An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1420, how much is invested at XXO each rate? 27. Financial planning After inheriting some money, a woman wants to invest enough to have an annual income of $5000. If she can invest $20,000 at 9% annual interest, how much more will she have to invest at 7% to achieve her goal? (See the table.) 36. Markup A merchant increases the wholesale cost of a surfboard by 30% to determine the selling price. If the surfboard sells for $588.90, find the wholesale cost. 37. Break-point analysis A machine to mill a brass plate has a setup cost of $600 and a unit cost of $3 for each plate manufactured. A bigger machine has a setup cost of $800 but a unit cost of only $2 for each plate manufactured. Find the break point. Туре Rate Amount Income 9% investment 0.09 20,000 .09(20,000) 7% investment 0.07 .07x 28. Investment A woman invests $37,000, part at 8% and the rest at 9% annual interest. If the 95% investment provides $452.50 more income than the 8% investment, how much is invested at each rate? 38. Break-point analysis A machine to manufacture fasteners has a setup cost of $1200 and a unit cost of $0.005 for each fastener manufactured. A newer machine has a setup cost of $1500 but a unit cost of only $0.0015 for each fastener manufactured. Find the break point. 29. Investment Equal amounts are invested at 6%, 7%, and 8% annual interest. If the three investments 39. Computer sales A computer store has fixed costs of $8925 per month and a unit cost of $850 for every computer it sells. If the store can sell all the comput- ers it can get for $1275 each, how many must be sold for the store to break even? (Hint: The break-even point occurs when costs equal income.) yield a total of $2037 annual interest, find the total investment. 30. Investment Aaron invested equal amounts of money at 5%, 7%, 9%, and 11% annual interest. If the four investments yielded a total of $1440 annual interest, find the total amount 40. Restaurant management A restaurant has fixed costs of $137.50 per day and an average unit cost of $4.75 for each meal served. If a typical meal costs $6, how many customers must eat at the restaurant each day for the owner to break even? invested. 31. Ticket sales A full-price ticket for a college bas- ketball game costs $2.50, and a student ticket costs $1.75. If 585 tickets were sold, and the total receipts were $1,217.25, how many tickets were student tickets? 32. Ticket sales Of the 800 tickets sold to a movie, 480 were full-price tickets costing $7 each. If the gate receipts were $4960, what did a student ticket cost? 41. Roofing houses Kyle estimates that it will take him 7 days to roof his house. A professional roofer estimates that it will take him 4 days to roof the same house. How long will it take if they work together? 33. Discount An iPad Air is on sale for $413.08. What was the original price of the iPad if it was dis- counted 8%? 42. Sealing asphalt One crew can seal a parking lot in 8 hours and another in 10 hours. How long will it take to seal the parking lot if the two crews work together? 34. Discount After being discounted 20%, a weather radio sells for $63.96. Find the original price. 35. Markup A business owner increases the wholesale cost of a kayak by 70% and sells it for $365.50. Find the wholesale cost. 43. Mowing lawns Julie can mow a lawn with a lawn tractor in 2 hours, and her husband can mow the same lawn with a push mower in 4 hours. How long will it take to mow the lawn if they work together? Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. ©Kalmatsuy/Shutterstock.com
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