Transcript Using linear equations to solve word problems

Using linear
equations to solve
word problems
Usually deal with changes over time.
Y intercept does not change
Slope does change
 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 over 100 miles. If Kim drives 400
miles, how much does she pay?
y=mx +/-b.
y = .11x +99
 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 the
slope. The slope is the rate of change:
$.11 per mile over 100 miles.
 Let x = the number of miles she drives
over 100 miles.
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.
Create a My Way
 Make up a word problem where
something is constant (does not change)
and something does change.
 State the y-intercept
 State the slope
 State what the variable (the “x”) is
Examples of Word
Problems for My Way
 Cell Phone: $50. monthly rate + .12
cents a minute over 300 minutes. Let x =
# of minutes over 300.
 T-shirt company charges $24. per order
plus $12.00 per shirt. Let x = the # of
shirts ordered.
Yoga classes: $10 for sign-up plus $5. per
class
STEPS IN SOLVING WORD
PROBLEMS WITH LINEAR
ALGEBRA
 1. Define the variable that you want to find with a let
statement. Let x = ….
 2. Create an equation that expresses the information
given in the problem’s scenario. Decide on the yintercept and the slope (rate of change)
 3. Solve your equation using algebraic methods.
 4. Consider if your answer is reasonable.
 5. Label your solution appropriately.
 6. Check your answer with the conditions given in the
problem.
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.