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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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sqdancefan
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.
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

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