Using linear equations to solve word problems
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Transcript 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.