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

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A paint store mixes 3/4 pint of red paint and 2/3 pint [#permalink] New post 10 Jan 2018, 10:44
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A paint store mixes \(\frac{3}{4}\) pint of red paint and \(\frac{2}{3}\) pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint [#permalink] New post 12 Jan 2018, 02:57
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1 pint of Perfectly purple paint contains
3/4 pint of red paint and 2/3 pint of blue paint
3/4 + 2/3 = 17/12 pint of R+B = 1 pint of Perfectly purple
34 pints of Perfectly purple contains 17/12*a(where a is a scale factor) of both Red and Blue paints
solve for a, a = 24. In total 24 pints of Red and blue paints is used for 34 pints of Perfectly purple
Red paint in pints = 3/4*24=18 (B)
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint [#permalink] New post 12 Jan 2018, 06:52
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Carcass wrote:



A paint store mixes \(\frac{3}{4}\) pint of red paint and \(\frac{2}{3}\) pint of blue paint to make a new paint color called Perfectly Purple. How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?

A. 1.42

B. 18.0

C. 36.13

D. 47.5

E. 48.12

Kudo for right answer and solution


Let R = # of pints of red paint needed
Let B = # of pints of blue paint needed

A paint store mixes 3/4 pint of red paint and 2/3 pint of blue paint to make a new paint color called Perfectly Purple
This tells us the RATIO of the volumes of paint needed.
That is: R/B = (3/4)/(2/3)
Cross-multiply to get: (2/3)(R) = (3/4)(B)
Eliminate the fractions by multiplying both sides by 12 to get: 8R = 9B
Rearrange to get: 8R - 9B = 0

How many pints of red paint would be needed to make 34 pints of Perfectly Purple paint?
We want the TOTAL volume to be 34 pints
So, we can write: R + B = 34

We now have the following system that we must solve for R:
8R - 9B = 0
R + B = 34

Take bottom equation and multiply both sides by 9 to get the following EQUIVALENT equation:
8R - 9B = 0
9R + 9B = 306

ADD the two equations to get: 17R = 306
Solve to get: R = 18
Answer: B

Cheers,
Brent
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint [#permalink] New post 15 Sep 2018, 01:44
May I know why when I use the equation 3/4R+2/3B=1 (i.e. 3/4 red plus 2/3 blue to make one pint of purple) and solve simultaneously with R+B=34, I get a different answer?
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint [#permalink] New post 15 Sep 2018, 12:16
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Runnyboy44 wrote:
May I know why when I use the equation 3/4R+2/3B=1 (i.e. 3/4 red plus 2/3 blue to make one pint of purple) and solve simultaneously with R+B=34, I get a different answer?



\(\frac{3}{4}R+\frac{2}{3}B=1\). This equation is incorrect. 1 pint cannot contain \(\frac{3}{4}\) Red and \(\frac{2}{3}\) Blue.

The correct equation is:

\(\frac{3}{4}R + \frac{2}{3}B = \frac{17}{12}\)

or \(9R + 8B=17\) multiplying 12 on both sides.
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Re: A paint store mixes 3/4 pint of red paint and 2/3 pint   [#permalink] 15 Sep 2018, 12:16
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