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A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint

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A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint  [#permalink]

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New post 14 Feb 2016, 03:35
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A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 34 pints of Perfect Pink paint?

A. 9
B. 16
C. 18
D. 25 1/3
E. 28 1/2

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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint  [#permalink]

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New post 15 Feb 2016, 20:02
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Bunuel wrote:
A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 34 pints of Perfect Pink paint?

A. 9
B. 16
C. 18
D. 25 1/3
E. 28 1/2


Hi,
3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink
so 17/12 pint requires 3/4 pint of red..
1 pint will require 3/4 * 12/17=9/17..
34 pints will require 9/17 * 34= 18 pints..


Second way..
get both red and white paints in same denominator...
3/4 + 2/3 = (9/12)+(8/12) pints..
from here we get the ratio of red:white = 9:8..
so in 34 pints red will be 9/(9+8) * 34 =18..


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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint  [#permalink]

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New post 17 Feb 2016, 22:23
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Hi All,

The answer choices in this question are 'spread out' enough that we can get the correct answer without having to do too much math.

We're given the 'recipe' for making Perfect Pink paint: 3/4 pint of red paint and 2/3 pint of white paint

3/4 = .75 pints
2/3 = .66666 pints

These two fractions are relatively close to one another, so when we make Perfect Pink paint, a little MORE than half will be red and a little LESS than half will be white. Since we're only making 34 pints of this paint (which is not a lot), the total amount that will be red paint will be just a little more than half of 34 - so a little more than 17. There's only one answer that makes sense...

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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint  [#permalink]

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New post 09 Jul 2017, 10:52
I am trying to do this question in the following way but i am not getting the answer
suppose we need x pints of red paint then we get the equation as
3/4x + 2/3 (34-x) = 34
solving this i am not getting the answer, is my approach right?
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint  [#permalink]

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New post 29 Sep 2018, 10:38
3/4+2/3=17/12 of pink paint made
So, to make 34 we need (34/17)*12=24
=>24 times red paint required =>24*3/4=18 C is the correct choice.
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint &nbs [#permalink] 29 Sep 2018, 10:38
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