Download Using linear equations to solve word problems

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 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 yintercept? $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.