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# and the yellow ones #y#.

Then we can say:

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

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

#w + y - y= 30 - y#

#w = 30 - y#

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

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

#358.5 - 11.95y + 12.50y = 364#

#358.5 + 0.55y = 364#

#358.5 - 0.55y - 358.5 = 364 - 358.5#

#0.55y = 5.5#

#(0.55y)/0.55 = 5.5/0.55#

#y = 10#

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

#w = 30 - 10#

#w = 20#