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:
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.
