Question

One day a store sold 20 sweatshirts. White ones cost​ $ 10.95 and yellow ones cost $ 13.50. In​ all, ​$262.35 worth of sweatshirts were sold. How many of each color were​ sold?

Answer 1

17 yellow sweatshirts were sold and 3 white sweatshirts were sold.

How did I get this?

First, we need to figure out what we know.
20 sweatshirts sold
White sweatshirts $10.95
Yellow sweatshirts $13.50
Total spent $262.35

$10.95W + $13.50Y = $262.35 
W + Y = 20 sweatshirts 

In both equations, the variables represent the amount of sweatshirts sold, which is unknown, but when we know the amount it will add up to $262.35.

Y = 20 - W so lets substitute that into the first equation

10.95w + 13.50(20 - W) = 262.35
Distribute the 13.50 into the parenthesis.

10.95w + 270 - 13.50w = 262.35
Combine like terms.

-2.55w + 270 = 262.35
Subtract both sides by 270, the left side will cancel out.

-2.55w = -7.65
Divide -2.55 by both sides to isolate the variable. 

W = -7.65/-2.55 
(W)hite = 3 sweatshirts 

Put 3 sweatshirts into our second equations.

Y = 20 - 3 
(Y)ellow = 17 sweatshirts

So, 17 yellow sweatshirts were sold and 3 white sweatshirts were sold.

Now, lets check our math by substituting the # of sweatshirts into our first equation.

$10.95(3) + $13.50(17) = $262.35
$32.85 + $229.50 = $262.35
$262.35 = $262.35 (correct!)