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A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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25 Mar 2005, 23:36

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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?

3:5 => 3+5=8 => divide 2 by 8 => its easier to think when we multiply the 2 by 10 => how many times fits 8 in 20. it is 2 and 1/2 times => because of the fact that we can also buy half gallons, it is already the answer.

3:5 => 3+5=8 => divide 2 by 8 => its easier to think when we multiply the 2 by 10 => how many times fits 8 in 20. it is 2 and 1/2 times => because of the fact that we can also buy half gallons, it is already the answer.

christoph, Can you be more brief, why do you say "divide 2 by 8" - Why 2?

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. 2 1/2 C. 3 D. 3 1/2 E. 4

Hi Rthothad, here a good explanations as to how the answer is 2.5

For every gallon you need 3/8 W and 5/8 B. For 2 gallons you need 3/4 W and 5/4 B.
Since the W and B are in gallon and half gallon tins, you need to purchase 1 gallon W and one and a half gallon of B. Total would be two and a half gallon.

3:5 => 3+5=8 => divide 2 by 8 => its easier to think when we multiply the 2 by 10 => how many times fits 8 in 20. it is 2 and 1/2 times => because of the fact that we can also buy half gallons, it is already the answer.

christoph, Can you be more brief, why do you say "divide 2 by 8" - Why 2?

...because 2 gallons are needed ! we combine 3 and 5 to 8 and look for the least common multiple => that is 24 => so normally it would be 3 gallons but we can also use half gallons so it is 2 * 0,8 + 1/2 * 0,8 = 2 => 2 + 1/2 => 2,5

Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]

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02 Aug 2017, 17:00

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