SOLUTION: You are given 2 cans of paint. The first can contains 60% yellow paint and 40% blue paint. The second can contains 30% yellow paint and 70% blue paint. How much paint fro

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Question 984107: You are given 2 cans of paint.
The first can contains 60%
yellow paint and 40% blue paint.
The second can contains 30%
yellow paint and 70% blue paint.
How much paint from each can
should you mix together in order
to obtain 4 gallons of paint which
is 50% yellow and 50% blue?
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Both cans have only "yellow" and "blue". This seems like a description of the typical simple two-part mixture type.

First Can, 60% Yellow
Second Can, 30% Yellow
An attempt at doing this solution in just one single variable:

Let v be how much gallons of the first can of 60% yellow.
Then 4-v is gallons of the second can at 30% yellow.

volumeYellow%2FvolumePaint=FractionYellow

%2860%2Av%2B30%2A%284-v%29%29%2F4=50

Immediately simplify if doing with the given values already present.
%286v%2B3%284-v%29%29%2F4=5

6v%2B12-3v=5%2A4
3v%2B12=20
3v=8
highlight%28v=8%2F3=2%262%2F3%29, gallons of the 60% yellow paint.
This means 1%261%2F3 of the 30% yellow paint.