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Solving Story Problems with Proportions

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Solving Story Problems

with Proportions

You need to set up a proportion when you are comparing two things…

- Such as:
- Miles per hour
- Cost per ounce
- Money per hour

- The first thing you should do is find the two things that the problem is comparing. Then write out your verbal model.
- Next, decide what you are looking for and define a variable.
- Set up your proportion and solve.
- Always answer in a complete sentence.

Example #1

Janice worked 22 hours last week and brought home $165. She worked 31 hours this week. How much money will she bring home this week?

What are the two things being compared?

hours and money

The verbal model:

X = money for this week

Unknown:

Proportion:

Answer:

Janice will bring home $232.50 this week.

Example #2

The airplane traveled 1037.5 miles in 2.5 hours. What was the airplane’s average rate of speed in miles per hour?

What are the two things being compared?

miles and hours

The verbal model:

Unknown:

x = number of miles per one hour

Proportion:

Answer:

The airplane traveled an average speed of 415 miles per hour.

Example #3

Henry answered 51 questions correctly and received an 85%. If Sydney received a 75%, how many questions did she answer correctly?

What are the two things being compared?

questions answered correctly and grade

The verbal model:

Unknown:

X = the number of questions Sydney answered correctly

Proportion:

Answer:

Sydney answered 45 questions correctly.

Example #4

The ABC Appliance Company can ship 310 refrigerators in 5 trucks. How many trucks will it take to ship 186 refrigerators?

What are the two things being compared?

refrigerators and trucks

The verbal model:

X = the number of trucks needed to ship 186 refrigerators

Unknown:

Proportion:

Answer:

It will take 3 trucks to ship 186 refrigerators.