Writing & Solving Equations given real World Problems Writing & Solving Equations given real World Problems Objectives: To solve word problems involving linear equations.

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA 1. Define the variable that you want to find with a ‘let’ statement. (V) 2. Identify the key information. (K) 3.Write a word equation. (W) 4.Write a numerical equation. (E) 5.Solve your equation using algebraic methods and label your solution appropriately. (S) 6.Check your answer with the conditions given in the problem and consider whether your answer is reasonable. (R) VIKINGS KNOW WHY EVERYONE SAILS RIGHT

EX 1 1) A video store charges $8 to rent a video game for five days. You must be a member to rent from the store, but the membership fee is free. A video game club in town charges only $3 to rent a game for five days, but membership in the club is $50 per year. Which rental plan is more economical? Step 1: Variable (V) Let x = # of video games rented per year Step 2: Key information (K) Video store: $8 to rent game for five days & free membership Video Game Club: $3 to rent game for five days & $50 membership

EX 1 STORE RENTAL FEE NUMBER RENTED CLUB MEMBERSHIP FEE NUMBER RENTED CLUB RENTAL FEE Step 3: Write word equation (W) Step 4: Write numerical equation (E)

EX 1 If you rent less than 10 video games a year, choose the Video Store. If you rent 10 video games a year choose either one. If you rent more than 10 video games a year, choose the Video Game Club. Step 5: Solve the equation (S)

EX 1 Yes, 10 is a reasonable solution since it is a positive number. It is also reasonable for someone to rent 10 games per year. It is reasonable that the Video club would be more economical if more games are rented since it has a large membership fee. Step 6: Conditions/reasonable

EX 2 1) The bill (parts and labor) for the repair of a car was $458. The cost of parts was $339. The cost of labor was $34 per hour. Write and solve an equation to find the number of hours of labor. Step 1: Variable (V) Let h = # of hours of labor Step 2: Key information (K) Bill was $458 Parts cost $339 Labor cost $34 per hour – 34h

EX 2 Step 3: Write word equation (W) Step 4: Write numerical equation (E) PARTS + LABOR = BILL

EX 2 The bill includes 3 ½ hours of labor. Step 5: Solve the equation (S)

EX 2 Yes, 3.5 is a reasonable solution since it is a positive number. 3.5 is a reasonable # of hours since it has to be multiplied by 34 and added to 339 to get the bill of $458 Step 6: Conditions/reasonable

EX 3 1) Tyler and Jonathan went to Howies Game Shack to play video games. Tyler had $50 and played on the xbox that costs $15 per hour. Jonathan arrived at Howies with $35 and played video games on the computer that costs $10 per hour. After how many hours will the two boys have the same amount of money left? How much money will they have left? Can they continue playing? Step 1: Variable (V) Let h = # of hours playing video games Step 2: Key information (K) Tyler – had $50, cost $15 per hour to play Jonathan – had $35, cost $10 per hour to play

EX 3 Step 3: Write word equation (W) Step 4: Write numerical equation (E) Tyler $ start with - $ spent = Jonathan $ start with - $ spent

EX 3 It took 3 hours of playing video games for the boys to have the same amount of money. Step 5: Solve the equation (S)

T = 50 – 15h & J = 35 – 10h represents the amount of money they have left after h hours. T = 50 – 15h = 50 – 15(3) = $5 So after 3 hours, they will each have $5 left. They cannot continue to play the xbox and computer because Tyler needs $15 to play for an hour and Jonathan needs $10 to play for the hour. They either will go home or they can combine their money and play for an hour on the computer together. How much money did they have after 3 hours? Will they continue to play games?

EX 3 Yes, 3 is a reasonable solution since it is a positive number. 3 is a reasonable # of hours to play video games. Step 6: Conditions/reasonable