Solving Word Problems with Variables on Both Sides

1. Solving Word Problems with Variables on Both Sides

2. Pedro and Maria each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal. • The first sentence doesn’t have any relevant information, so cross it out.

3. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many will their accounts be equal. • What is the question asking for? • If we don’t know something what do we call it? weeks x

4. Pedro opened his account with $710 and withdrew per week. Maria opened her account with $570 and withdrew weekly. In how many weeks will their accounts be equal. • What numbers go with x (weeks)? • We have two numbers that go with x, therefore we have two equations. • When we have 2 equations we set them equal to each other $35 $25

5. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal. • The question asks when they will be equal, so we use an equals sign • Replace the first m with $35 and the second m with $25 25 m x + b 35 m x + b =

6. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal. • They are both taking money away from their account, so both values of m have to be negative • We then replace the b on Pedro’s equation with $710 and Maria’s with $570 - - 25 x + b + 570 35 x + b +710 =

7. We now have an equation we can solve for! • Add 35x to both sides • Subtract 570 from both sides • Divide by 10 -35x + 710 140 14 x = -25x 10x + 570 +35x+35x -570-570 10 10

8. Pedro and Maria each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Pedro opened his account with $710 and withdrew $35 per week. Maria opened her account with $570 and withdrew $25 weekly. In how many weeks will their accounts be equal. • x = weeks, so in 14 weeks their accounts will be equal 14 = x

9. 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? You Try!

10. 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?

11. Nilda has $250 in her savings account. She plans to save $15 per week from her salary. Iona 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?

12. 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.