A certain shade of gray paint is obtained by mixing 3 parts : PS Archive
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# A certain shade of gray paint is obtained by mixing 3 parts

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

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14 Aug 2004, 08:13
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A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of back 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) 5/2 (C)3 (D) 7/2 (E) 4

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14 Aug 2004, 08:47
In 2 gallons we have 3/4 (or 0.75 gallaons) of white and 5/4 (1.25
gallaons) of black.

However, since the paints are sold only in 1 gallon or .5 gallons, then minimum White we are forced to buy is 1 gallon and the minimum Black we are forced to buy is 1.50 gallons - totalling to 2.5 gallons.

2.5 = 5/2. Answer is B
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14 Aug 2004, 10:04
3W + 5B = 8G
We need only 2G so divide everything by 4
We get 3/4W + 5/4B = 2G
Paint is sold only in .5 or 1 gallon so multiple everything by 2 to get halves.
3/2W + 5/2B = 4G
As you can see, you need at least 5/2 Black paint and that is the minimum you need to purchase to complete the mixture
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Paul

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15 Aug 2004, 23:20
A certain shade of gray paint is obtained by mixing 3 parts of white
paint with 5 parts of back 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) 5/2 (C)3 (D) 7/2 (E) 4

You need 2 gallons of the mixture, with ratio white:black = 3:5

So white = 3/8*2 = 0.75 gallon
black = 5/8*2 = 1.25 gallon

So the least amount is to buy 1 gallon of white paint and 1.5 gallons of black paint
giving you a total of 2.5 gallons
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16 Aug 2004, 06:03
I found this ambiguous a bit.

Is the query about the gray paint or any of black or white paints to be purchased?

It is clear that for two gallons : W : B = 0.75 : 1.25 That means for 4 gallons = 1.5 : 2.5

The least amount of White paint is 1.5.
The least amount of Black paint is 2.5.
The least amount of Gray paint is 4.

What is the answer - B or E? I got confused a bit.

chunjuwu wrote:
A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of back 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) 5/2 (C)3 (D) 7/2 (E) 4

_________________

Awaiting response,

Thnx & Rgds,
Chandra

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16 Aug 2004, 08:50
thanks all, I see it.

But, mallelac, why needs 4 gallon?
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16 Aug 2004, 22:37
Actually, I am flummoxed by the query a bit.

Is the query about the purchase of gray paint or black/white paint?

I have just now looked at the answers given by 'venksune' and 'paul'. Though both arrived at the same answer, the way they interpreted the problem is completely different.

I appreciate if I am explained the query first. Thanks in advance.

chunjuwu wrote:
thanks all, I see it.

But, mallelac, why needs 4 gallon?

_________________

Awaiting response,

Thnx & Rgds,
Chandra

16 Aug 2004, 22:37
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