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# Equations in Word Problems Help

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By — McGraw-Hill Professional
Updated on Sep 22, 2011

## Equations in Word Problems

Equations can be used to solve word problems in algebra.

After reading the problem:

• Step 1 Represent one of the unknown quantities as x and the other unknown by an algebraic expression in terms of x.
• Step 2 Write an equation using the unknown quantities.
• Step 3 Solve the equation for x and then find the other unknown.
• Step 4 Check the answers.

#### Example 1

One number is 8 more than another number. The sum of the two numbers is 114. Find the numbers.

#### Solution 1

Hence, one number is 53 and the other number is 61.

Step 4 Check: 53 + 61 = 114.

#### Example 2

A carpenter cuts a board 72 inches long into two pieces. One piece is twice as long as the other. Find the lengths of the pieces.

#### Solution 2

Hence, one piece is 24 inches long and the other piece is 48 inches long.

Step 4 Check: 24 inches + 48 inches = 72 inches

#### Example 3

\$40 in tips is to be divided among three food servers. The first server gets twice as much as the second server since he worked twice as long; the third server gets \$7. Find the amount each server received.

#### Solution 3

Hence, the first server received \$22, the second server received \$11, and the third server received \$7.

Step 4 Check: \$22 + \$11 + \$7 = \$40

### Equations in Word Problems Practice Problems

#### Practice

1. A stick 56 inches long is broken into two pieces so that one piece is 28 inches longer than the other piece. Find the length of each piece.

2. A person made two purchases. One purchase costs four times as much as the other purchase. The total cost of both purchases was \$28. Find the cost of each purchase.

3. The difference between two numbers is 12. Find the values of each of the numbers if their sum is 28.

4. A mother is 4 times older than her daughter. In 14 years, she will be twice as old as her daughter. Find their ages now.

5. A house is worth four times as much as the lot it is built on. If the sum of the values of the house and lot is \$156,000, find the value of each.

#### Answers

1. 14 inches, 42 inches

2. \$5.60, \$22.40

3. 8, 20

4. mother's age = 28; daughter's age = 7

5. lot's value = \$31,200; house's value = \$124,800

Practice problems for this concept can be found at: Expressions And Equations Practice Test.

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