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**Solving Word Problems with Variables on Both Sides**

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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.

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**Pedro opened his account with $710 and withdrew $35 per week**

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

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**Pedro opened his account with $710 and withdrew. per week**

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

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**Pedro opened his account with $710 and withdrew $35 per week**

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 =

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**Pedro opened his account with $710 and withdrew $35 per week**

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 + 570 + b 35 x +710 + b =

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**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 x = -25x 10x + 570 +35x x

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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

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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!

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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?

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**Nilda has $250 in her savings account**

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?

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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.

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