Using linear equations to solve word problems

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Using linear equations to solve word problems Essential question: How do I create and solve an equation to solve a word problem?

Review of Linear Equations Remember that y = mx + b m is the slope (rise over run) b is the y-intercept

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA 1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change. This is the constant or y-intercept, b. 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be the coefficient of x. 5. Plug what you know into the equation y = mx + b 6. Solve the problem 7. Make sure your solution is reasonable.

The y-intercept does not change, so it is the constant (no variable) The y-intercept does not change, so it is the constant (no variable). The slope goes with a value that does change, so it is multiplied by the variable x. Example: Kim wants to rent a car on the Big Island. Mr. Lee’s Rentals rents cars for $99.00 for one week plus $0.11 per mile. If Kim drives 400 miles, how much does she pay?

y=mx + b. The weekly rental rate does not change. It is the y-intercept, and it’s $99.00. The amount of miles changes, so it is multiplied by the slope. The slope is the rate of change: $.11 per mile.

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA 1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change. This is the constant or y-intercept, b. $99 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be the coefficient of x (the slope). .11 5. Plug what you know into the equation y = mx + b y = .11x + 99 6. Solve the problem. Plug in 400 miles for x y = .11(400) + 99 y = $143 7. Make sure your solution is reasonable.

Example #2: y=5x+10 Bobby charges $10. per lawn he mows, and an additional $5. per hour. What does not change? What is the y-intercept? $10.00 per lawn What changes? What is the slope? The $5. per hour depending on how many hours it takes to mow the lawn Let x = the number of hours it takes to mow a lawn.

STEPS IN SOLVING WORD PROBLEMS WITH LINEAR ALGEBRA 1. Find out what the total will be. Define the total as y. 2. What is the starting point or what doesn’t change. This is the constant or y-intercept, b. 3. Decide what varies. Let this amount be x. 4. Decide if x is multiplied by an amount. This will be the coefficient of x. 5. Plug what you know into the equation y = mx + b 6. Solve the problem 7. Make sure your solution is reasonable.

Practice Problems Exercise #1: At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they all had the same price.