Download CHAPTER 3: Applications of Algebra Section 3.2: Solving Application Problems Topics: A.

MATH 0960
Section 3.2 Notes
CHAPTER 3: Applications of Algebra
Section 3.2: Solving Application Problems
Topics:
A. Set up and solve number application problems.
B. Set up and solve rate problems.
C. Set up and solve percent problems.
Preliminary: Follow the steps below to solve application problems from sections 3.2 and
3.3.
1. Assign a variable and write all expressions in terms of that variable. (1 point)
2. Write an equation relating the expressions. (1 point)
3. Solve the equation. (1 point)
4. Answer the question (include any units!). (1 point)
A. Set up and solve number application problems.
 What does a problem look like?
Example: Define a variable, then set up an equation that can be used to solve the
problem. Solve the equation and answer the question asked.
The larger of two numbers is two more than four times the smaller. The larger
number minus the smaller number is 38. What are the numbers?
Answer:
smaller number
larger number
Smaller number = 12, larger number = 50
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MATH 0960
Section 3.2 Notes
B. Set up and solve rate problems.
 What does a problem look like?
Example: Define a variable, then set up an equation that can be used to solve the
problem. Solve the equation and answer the question asked.
Dave’s Lanes charges $4 for shoe rental and $4 per game. Holiday Bowl charges $10
for shoe rental and $3 per game. How many games would Lisa have to bowl for the
two alleys to charge her the same amount?
Answer:
number of games
Dave’s Lanes cost
Holiday Bowl cost
6 games

What do I need to know?
o In many of these problems you need to find an expression for total cost. In
that case cost equals flat rate plus variable rate.
o When two competing companies are involved write an expression for the
cost at each and set them equal.
C. Set up and solve percent problems.
 What does a problem look like?
Example: Define a variable, then set up an equation that can be used to solve the
problem. Solve the equation and answer the question asked.
The output of a factory after a 5% increase in production is 25,200 units per week.
What was the factory’s production output before the increase?
Answer:
output before increase
output after increase
24,000 units
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