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?

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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?

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Answer 1 · 2016-11-20T17:30:28

The store sold 16 white and 12 yellow sweatshirts.

Explanation:

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

$w + y = 28$ $w + y = 28$

Solving for $w$ $w$ gives:

$w + y - y = 28 - y$ $w + y - y =28 - y$

$w = 28 - y$ $w = 28 - y$

We also know and can write:

$9.95 w + 13.50 y = 321.20$ $9.95w + 13.50y = 321.20$

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

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

$278.6 - 9.95 y + 13.50 y = 321.20$ $278.6 - 9.95y + 13.50y = 321.20$

$278.6 + 3.55 y = 321.20$ $278.6 + 3.55y = 321.20$

$278.6 + 3.55 y - 278.6 = 321.20 - 278.6$ $278.6 + 3.55y - 278.6 = 321.20 - 278.6$

$3.55 y = 42.6$ $3.55y = 42.6$

$\frac{3.55 y}{3.55} = \frac{42.6}{3.55}$ $(3.55y)/3.55 = 42.6/3.55$

$y = 12$ $y = 12$

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

$w = 28 - 12$ $w = 28 - 12$

$w = 16$ $w = 16$

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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?

1 Answer

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