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

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Answer 1 · 2018-04-08T16:11:39

14 inches of wire

Set up a proportion of inches of wire:cents

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

$\frac{17}{51} = \frac{w}{42} \to$ $17/51=w/42 rarr$ Put them in fraction form

$\frac{1}{3} = \frac{w}{42} \to$ $1/3=w/42 rarr$ 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

$w = 14$ $w=14$

Or you could cross multiply:

$1 \cdot 42 = w \cdot 3$ $1*42=w*3$

$42 = 3 w$ $42=3w$

$w = 14$ $w=14$