**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*.

**Examples**

**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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