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?

Question

Mathematics

Harper Hayes

29 January, 10:27

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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Answers (2)

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Stevenson · Answer 1

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

Kaiya · Answer 2

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.