Question 115263: Painting:
A painter wishes to mix paint worth $15 per gallon with paint worth $18 per gallon to make a 12 gallon mixture worth $16.75 per gallon. How many gallons of each should he mix?
Answer by ganesh(20)   (Show Source):
You can put this solution on YOUR website! Let x gallons of $15 paint and y gallons of $18 paint are mixed to get 12 gallons of $16.75 paint.
From this, we come to know, x + y = 12.
Also, the rate of 12 gallons mixture paint = 12 * 16.75 = $201.
This should be equal to 15x + 18y.
So, we get 15x + 18y = 201 -----------(1)
We already have x + y = 12 -----------(2)
(2)* 15 gives, 15x + 15y = 180 -------(3)
(1) - (3) gives, 3y = 21.
This gives, y = 7.
Plug in (2). We get, x = 5.
So, 5 gallons of $15 paint and 7 gallons of $18 paint gives a mixture of 12 gallons of $16.75 paint.
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