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A certain shade of gray paint is obtained by mixing 3 parts [#permalink]
25 Apr 2006, 12:18

. A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B)
(C) 3
(D)
(E) 4
Can somebody please explian

From the Question
2 W + 5 B = 7G
To make 2G we need at least the following
W = 4/7= 0.5.. G
B = 10/7 = 1.4...
Since the amount is availabe only in 0.5 or 1 G
W = 1 B= 1.5 Total = 2.5

But since you have answer Choices have 3 the answer should be C.

White in the mixture is 3/8*Gallons
Black in the mixture is 25/8*Gallons

For 2 gallons of mixture, white needed is 3/4 G, and Black needed is 5/4 G.
3/4 Gallon, just buy one 1 gallon of white, and for black(5/4G), buy one 1 g and one 0.5 g.

We're told we need 2 gallons of gray paints. So these 8 parts represent 2 gallons. Therefore, 1 part = 0.25 gallons. We can now tell that we need 0.75 gallons of white paint and 1.25 gallons of black paint.

The paints are available in 1 gallon or 1/2 gallon cans. For the white paint, we can't buy the 1/2 gallon can as we need 0.75 gallons. So we will need to buy a 1 gallon can of white paint. The same reason applies to the black paint, we will ned a 1 gallon can of black paint, and a 1/2 gallon can of black paint.

The least amt we need to purchase is therefore 2.5 gallons.