# Suppose that 17 inches of wire costs 51 cents. At the same rate, how many inches of wire can be bought for 42 cents?

Apr 8, 2018

14 inches of wire

#### Explanation:

Set up a proportion of inches of wire:cents

$17 : 51 = w : 42 \rightarrow w$ represents the unknown amount of wire that can be bought for 42 cents

$\frac{17}{51} = \frac{w}{42} \rightarrow$ Put them in fraction form

$\frac{1}{3} = \frac{w}{42} \rightarrow$ The first fraction can be simplified (17 is a factor of 51)

Since 3 is being multiplied by 14 to get 42, we can multiply 1 by 14 to get w

$w = 14$

Or you could cross multiply:

$1 \cdot 42 = w \cdot 3$

$42 = 3 w$

$w = 14$