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 PurpleThis 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 = 0How 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 = 34We now have the following system that we must solve for R:

8R - 9B = 0R + B = 34Take bottom equation and multiply both sides by 9 to get the following EQUIVALENT equation:

8R - 9B = 09R + 9B = 306ADD the two equations to get: 17R = 306

Solve to get: R = 18

Answer: B

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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