6.3 Applications of Algebra 319 7. 6, decreased by 4 times y − y 6 4 8. 7 times x, increased by 4 x7 4 + 9. The product of 8 and w, increased by 9 w8 9 + 10. 8, increased by 5 times x x 8 5 + 11. 6 more than 4 times x x4 6 + 12. 5 less than twice a number x2 5 − 13. The quotient of z and 13, decreased by 4 z 13 4 − 14. 9 less than the product of 7 and w w7 9 − 15. 12 decreased by s, divided by 4 s 12 4 − 16. The sum of 8 and t, divided by 2 t 8 2 + 17. Three times the sum of a number and 7 x 3( 7) + 18. 4− times the difference between x and 1. x 4( 1) − − In Exercises 19–30, write an equation and solve. 19. The sum of a number and 11 is 24. x 11 24; 13 + = 20. The difference between a number and 6 is 9. x 6 9; 15 − = 21. The product of 7 and a number is 56. x7 56; 8 = 22. The quotient of a number and 3 is 15. = x 3 15; 45 23. Ten less than four times a number is 42. x4 10 42; 13 − = 24. Fourteen increased by 6 times a number is 32. x 14 6 32; 3 + = 25. Twelve more than 4 times a number is 32. x4 12 32; 5 + = 26. Eight less than the product of 3 and a number is 6 times the number, increased by 10. x x 3 8 6 10; 6 − = + − 27. A number increased by 6 is 3 less than twice the number. x x 6 2 3; 9 + = − 28. The quotient of a number and 4 is 12 less than the number. x x 4 12; 16 = − 29. A number increased by 10 is 2 times the sum of the number and 3. x x 10 2( 3); 4 + = + 30. Three times the difference of a number and 4 is 6 more than the number. x x 3( 4) 6; 9 − = + Problem Solving In Exercises 31– 42, set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). When necessary, round answers to the nearest hundredth. 31. MODELING—Salary Plus Commission Maria is the manager at the Ruiz Auto center. She is paid a salary of $375 per week plus a commission of 12% of the sales amount at the center that week. Maria has a goal to earn a total of $1500 per week, including salary and commission. What is the sales amount needed for Maria to reach her goal? x 375 0.12 1500; $9375 + = 32. MODELING—Hourly Wage Plus Tips Camden works as a banquet server. He is paid $7.50 per hour plus a tip $ $ of 20% of the amount charged for all food and beverages served. One evening, Camden worked for 4 hours and received total pay of $142. What was the amount charged for the food and beverages? x 7.50(4) 0.20 142; $560 + = 33. MODELING—Investment Franklin received an inheritance of $20,000. If he wants to invest three times as much money in stocks as in mutual funds, how much money should Franklin invest in mutual funds and in stocks? x x3 20,000; $5000 + = in mutual funds and $15,000 in stocks 34. MODELING—Scholarship Donation Andrea donates a total of $1000 for scholarships at Nassau Community College for liberal arts students and for business students. The amount she donates for scholarships for liberal arts students is three times the amount she donates for scholarships for business students. Determine the amount she donates for each type of scholarship. x x3 1000; $250 + = for business, $750 for liberal arts 35. MODELING—Dimensions of a Deck Jim is building a rectangular deck and wants the length to be 2 ft greater than the width. What will be the dimensions of the deck if the perimeter is to be 52 ft? w w 2 2( 2) 52; + + = width: 12 ft, length: 14 ft 36. MODELING—Picture Frame Marty is building a rectangular picture frame and has 42 inches of framing material to work with. What should be the dimensions of the frame if Marty wants the width to be 5 inches less than the length? l l 2 2( 5) 42; + − = length: 13 in., width: 8 in. 37. MODELING—Jet Skiing At Action Water Sports of Ocean City, Maryland, the cost of renting a Jet Ski is $42 per half hour, which includes a 5% sales tax. Determine the cost of a half hour Jet Ski rental before tax. x x 0.05 42; $40 per half hour + = 38. MODELING—SUV Battery When Brittany purchased a new battery for her SUV, she paid 7% sales tax plus a $5 battery recycling fee. If the total cost Brittany paid was $208.30, determine the cost of the battery before the sales tax and the recycling fee. x x 0.07 5 208.30; + + = $190 39. MODELING—Reimbursed Expenses When sales representatives for PT Pharmaceuticals drive to out-oftown meetings that require an overnight stay, they receive $150 for lodging plus $0.50 per mile driven. How many miles did Joe drive if PT reimbursed him $255 for an overnight trip? x 150 0.50 255; 210 miles + = 40. MODELING—Custom Printing Kobe has written a book and wishes to use a custom printer to print copies of his book. There is a one-time setup fee of $250 plus a fee of $9.50 per book printed. If the total cost to Kobe was $3575, how many copies of the book were printed? x 250 9.50 3575; + = 350 copies $ $ $ $ $ $ Halfpoint/Shutterstock
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