Word Problems Involving the Distributive Property

The Distributive Property states that, for all real numbers x, y, and z,

x(y + z) = xy + xz.

This very important property is frequently used in word problems.

Example 1:

Rico's MP3 player holds songs of three different genres: grindcore, zydeco, and kuduro. There are 5 times as many grindcore tracks as there are zydeco tracks, and there are 7 times as many kuduro tracks as there are zydeco tracks. Let x represent the number of zydeco tracks. Write an expression for the total number of tracks on the MP3 player, and simplify it.

Multiply the number of zydeco tracks by 5 to get the number of grindcore tracks.

5x

Multiply the number of zydeco tracks by 7 to get the number of kuduro tracks.

7x

Add up the numbers of all the tracks.

x + 5x + 7x

Simplify using the distributive property.

= (1 + 5 + 7)x

= 13x

So, Rico's MP3 player holds 13x tracks.

Example 2:

A volleyball uniform costs $13 for the shirt, $11 for pants, and $8 for socks. Write two equivalent expressions for the total cost of 12 uniforms. Then find the cost.

Write an expression for the cost of 1 uniform, add $13, $11 and $8.

$13 + $11 + $8

Write an expression for the cost of 12 uniforms, multiply 12 by the cost of 1 uniform.

12($13 + $11 + $8)

Simplify using the distributive property.

= 12 · 13 + 12 · 11 + 12 · 8

= 156 + 132 + 96

Now Add.

= 384

So, the total cost of 12 uniforms is $384.