Solving Word Problems with Variables on Both Sides

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Solving Word Problems with Variables on Both Sides

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Solving Word Problems with Variables on Both Sides

Peter and Maggie each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Peter opened his account with $710 and withdrew $35 per week. Maggie opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal.

710 - 35W = 570 - 25W (-570) + 35W =(-570) + 35W 140 = 10W /10 = /10 Peter and Maggie each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Peter opened his account with $710 and withdrew $35 per week. Maggie opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal. 710 - 35W = 570 - 25W (-570) + 35W =(-570) + 35W 140 = 10W /10 = /10 14 WEEKS

The Magic Carpet charges $90 for installation and $9 per square yard of carpeting. The Carpeteria’s installation price is $50 but the store charges $13 for each square yard. For what number of square yards of carpeting will the cost, including installation, be the same for both stores?

90 + 9y = 50 + 13y (-50) - 9y = (-50) - 9y 40 = 4y /4 = /4 The Magic Carpet charges $90 for installation and $9 per square yard of carpeting. The Carpeteria’s installation price is $50 but the store charges $13 for each square yard. For what number of square yards of carpeting will the cost, including installation, be the same for both stores? 90 + 9y = 50 + 13y (-50) - 9y = (-50) - 9y 40 = 4y /4 = /4 10 sq. yards of carpeting

Prestige Car Rentals charges $44 per day plus 6¢ per mile to rent a mid-sized vehicle. Gateway Auto charges $35 per day plus 9¢ per mile for the same car. For what number of miles will both companies charge the same price?

44 + .06m = 35 + .09m (-35) - .06m = (-35) - .06m 9 = .03m /.03 /.03 Prestige Car Rentals charges $44 per day plus 6¢ per mile to rent a mid-sized vehicle. Gateway Auto charges $35 per day plus 9¢ per mile for the same car. For what number of miles will both companies charge the same price IF THE CAR IS RENTED FOR ONLY ONE DAY? 44 + .06m = 35 + .09m (-35) - .06m = (-35) - .06m 9 = .03m /.03 /.03 300 MILES

Nancy has $250 in her savings account Nancy has $250 in her savings account. She plans to save $15 per week from her salary. Caty has only $200 in her account but can save $20 a week from her paycheck. How many weeks will it take before the amount in each savings account is the same?

250 + 15w = 200 + 20w (-200) - 15w = (-200) - 15w 50 = 5w /5 /5 Nancy has $250 in her savings account. She plans to save $15 per week from her salary. Caty has only $200 in her account but can save $20 a week from her paycheck. How many weeks will it take before the amount in each savings account is the same? 250 + 15w = 200 + 20w (-200) - 15w = (-200) - 15w 50 = 5w /5 /5 10 WEEKS

A sales person in a stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250 plus a commission of $25 for each stereo sold. The other plan offers no salary but pays $50 commission on each stereo sold. How many stereos must the sales person sell to make the same amount of money under both plans?

250 + 25s = 50s - 25s = -25s 250 = 25s /25 = /25 10 STEREOS A sales person in a stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250 plus a commission of $25 for each stereo sold. The other plan offers no salary but pays $50 commission on each stereo sold. How many stereos must the sales person sell to make the same amount of money under both plans? 250 + 25s = 50s - 25s = -25s 250 = 25s /25 = /25 10 STEREOS