Question

a rug is made by weaving 20 lb of yarn that is 60% wool with a yarn that is 25% wool. how many pounds of the yarn that is 25% wool must be used if the finished rug is to be 39% wool.

Explanation:

Step1: Set up the equation

Let $x$ be the number of pounds of the 25% - wool yarn. The amount of wool in the 60% - wool yarn is $0.6\times20$ pounds, the amount of wool in the 25% - wool yarn is $0.25x$ pounds, and the total amount of yarn is $(20 + x)$ pounds with 39% wool, so the amount of wool in the final mixture is $0.39(20 + x)$ pounds. Then the equation is $0.6\times20+0.25x=0.39(20 + x)$.

Step2: Expand the right - hand side

$0.6\times20+0.25x=0.39\times20+0.39x$.
$12 + 0.25x=7.8+0.39x$.

Step3: Move the $x$ terms to one side

$12-7.8=0.39x - 0.25x$.
$4.2 = 0.14x$.

Step4: Solve for $x$

$x=\frac{4.2}{0.14}=30$.

Answer:

30