**Ratios and Proportions in Word Problems**

*In order to solve word problems using proportions:*

*Step 1 Read the problem*.*Step 2 Identify the ratio statement*.*Step 3 Set up the proportion*.*Step 4 Solve for x*.

In problems involving proportions, there will always be a ratio statement. It is important to find the ratio statement and then set up the proportion using the ratio statement. Be sure to keep the identical units in the numerators and denominators of the fractions in the proportion.

**Examples**

**Example 1**

An automobile travels 176 miles on 8 gallons of gasoline. How far can it go on a tankful of gasoline if the tank holds 14 gallons?

**Solution 1**

The ratio statement is:

so the proportion is:

Solve:

Hence, on 14 gallons, the automobile can travel a distance of 308 miles.

**Math Note:** Notice in the previous example that the numerators of the proportions have the same units, miles, and the denominators have the same units, gallons.

**Example 2**

If it takes 16 yards of material to make 3 costumes of a certain size, how much material will be needed to make 8 costumes of that same size?

**Solution 2**

The ratio statement is:

The proportion is:

Hence, yards or yards should be purchased.

**Ratios and Proportions in Word Problems Practice Problems**

**Practice**

1. If 5 pounds of grass seed will cover 1025 square feet, how many square feet can be covered by 15 pounds of grass seed?

2. If a homeowner pays $8000 a year in taxes for a house valued at $250,000, how much would a homeowner pay in yearly taxes on a house valued at $175,000?

3. If a person earns $2340 in 6 weeks, how much can the person earn in 13 weeks at the same rate of pay?

4. If 3 gallons of waterproofing solution can cover 360 square feet of decking, how much solution will be needed to cover a deck that is 2520 square feet in size?

5. A recipe for 4 servings requires 6 tablespoons of shortening. If the chef wants to make enough for 9 servings, how many tablespoons of shortening are needed?

**Answers**

1. 3075 square feet

2. $5600

3. $5070

4. 21 gallons

5. 13 or 13.5 tablespoons

Practice problems for this concept can be found at: Ratios and Proportions Practice Test.

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