Question

One day a store sold 28 sweatshirts. White ones cost $9.95 and yellow ones cost $13.50. In all, $321.20 worth of sweatshirts were sold. How many of each color were sold?

Answer 1

The store sold 16 white and 12 yellow sweatshirts.

Explanation:

Let's call the number of white sweatshirts sold `w` and the number of yellow sweatshirts sold `y`. Because we know there were a total of 28 sweatshirts sold we can write:

`w + y = 28`

Solving for `w` gives:

`w + y - y =28 - y`

`w = 28 - y`

We also know and can write:

`9.95w + 13.50y = 321.20`

From the first equation we can substitute `28 - y` for `w` in the second equation and solve for `y`

`9.95(28 - y) + 13.50y = 321.20`

`278.6 - 9.95y + 13.50y = 321.20`

`278.6 + 3.55y = 321.20`

`278.6 + 3.55y - 278.6 = 321.20 - 278.6`

`3.55y = 42.6`

`(3.55y)/3.55 = 42.6/3.55`

`y = 12`

We can now substitute `12` for `y` in the solution to the first equation and calculate `w`:

`w = 28 - 12`

`w = 16`