One day a store sold 30 sweatshirts. White ones cost $11.95 and yellow ones cost $12.50. In all, $364.00 worth of sweatshirts were sold. How many of each color were sold?

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Answer 1 · 2016-11-17T14:50:32

There were 10 yellow and 20 white sweatshirts sold by the store.

Let's call the white sweatshirts $w$ $w$ and the yellow ones $y$ $y$ .

Then we can say:

$w + y = 30$ $w + y = 30$ and $11.95 w + 12.50 y = 364$ $11.95w + 12.50y = 364$

Solve the first equation for $w$ $w$ while keeping the equation balanced:

$w + y - y = 30 - y$ $w + y - y= 30 - y$

$w = 30 - y$ $w = 30 - y$

Substitute $30 - y$ $30 - y$ into the second equation for $w$ $w$ and solve for $y$ $y$ while keeping the equation balanced:

#11.95(30 - y) + 12.50y = 364.

$358.5 - 11.95 y + 12.50 y = 364$ $358.5 - 11.95y + 12.50y = 364$

$358.5 + 0.55 y = 364$ $358.5 + 0.55y = 364$

$358.5 - 0.55 y - 358.5 = 364 - 358.5$ $358.5 - 0.55y - 358.5 = 364 - 358.5$

$0.55 y = 5.5$ $0.55y = 5.5$

$\frac{0.55 y}{0.55} = \frac{5.5}{0.55}$ $(0.55y)/0.55 = 5.5/0.55$

$y = 10$ $y = 10$

Substitute $10$ $10$ for $y$ $y$ in the result of the first equation and solve for $w$ $w$

$w = 30 - 10$ $w = 30 - 10$

$w = 20$ $w = 20$