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A certain shade of gray paint is obtained by mixing 3 parts [#permalink]
29 May 2010, 12:11

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55% (hard)

Question Stats:

58% (02:29) correct
42% (01:48) wrong based on 344 sessions

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 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

2 gallon of gray paint needs \(2*\frac{3}{3+5}=2*\frac{3}{8}=\frac{3}{4}\) gallons of white paint and \(2*\frac{5}{8}=\frac{5}{4}\) gallons of black paint.

To get \(\frac{3}{4}=0.75\) gallons of white paint we should purchase at least 1 gallon of white paint; To get \(\frac{5}{4}=1.25\) gallons of black paint we should purchase at least 1.5 gallons of black paint.

Doesn't 3 parts of white paint with 5 parts of black paint. play any role... plzz explain..im missing somewhere..

thanks

Gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint --> total 8 parts --> white 3/8 and black 5/8 --> 2 gallon of gray paint needs \(2*\frac{3}{8}=\frac{3}{4}\) gallons of white paint and \(2*\frac{5}{8}=\frac{5}{4}\) gallons of black paint.

Re: Mixture Problem [#permalink]
22 Jul 2010, 07:49

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TheSituation wrote:

I've been banging my head against the wall on this one... someone please give me a simple straightforward solution and assurance that it was a very difficult question lol.

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) 2.5 (C) 3 (D) 3.5 (E) 4

You need .75 gallons of white but since it comes in 1/2 or 1 you need 1 gallon You need 1.25 gallons of black but since it comes in 1/2 or 1 you need 1.5

Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]
13 Jul 2013, 22:20

Given W:B = 3:5 That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture. But we want least amount of white & black paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio, 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce 0.75: 1.25 gives 1+1.5 = 2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure 0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable. So correct ans is 2.5 gallons. B

Re: A certain shade of gray paint is obtained by mixing 3 parts [#permalink]
25 Nov 2014, 06:03

Expert's post

plaverbach wrote:

[...]in order to measure out the portions needed for the mixture?

How can you measure 0,75 gallons if you have only buckets of 0,5 and 1 gallons?

My answer: 2 cans of 1 gallon and 1 half can of black 1 can and a half of white result: 4 gallons!

Unless you have an other bottle (or any thing to measure), you cannot separate 0,75 gallons! Bunuel

Please re-read the solution.

To get 2 gallons of gray paint we need \(\frac{3}{4}\) gallons of white paint and \(\frac{5}{4}\) gallons of black paint.

To get \(\frac{3}{4}=0.75\) gallons of white paint we should purchase at least 1 gallon of white paint; To get \(\frac{5}{4}=1.25\) gallons of black paint we should purchase at least 1.5 gallons of black paint.