5 September, 21:22

# 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?

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1. 5 September, 21:27
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Grey : white : total

3 : 5 : 8

8parts = 2 gallon

1 part = 1/4 gallon

3 x 1/4 : 5 x 1/4 : 8 x 1/4

Grey : white : total

3/4 : 5/4 : 2

3/4 gallon of grey paint is needed, so we need to buy 1 gallon of grey

5/4 gallon of white paint is needed, so we need to buy 1.5 gallon of whilte
2. 5 September, 23:22
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3/8 of the mixture is white; 5/8 is black. Then for 2 gallons of mixture,

... (3/8) * 2 gal = 3/4 gal

of white paint are needed, and

... (5/8) * 2 gal = 5/4 gal

of black paint are needed.

Rounding up to the nearest 1/2 gallon,

... 1 gallon of white and 1 1/2 gallons of black must be purchased, for a total of 2 1/2 gallons of paint.