MathRevolution wrote:

The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity of cashews as the first mixture but the peanuts’ quantity of the second mixture is 8 pounds fewer than that of the first mixture. If the ratio of the peanuts to cashews is 7 to 3 in the second mixture, what is the amount of the peanuts quantity in the first mixture, in pounds?

A. 24

B. 28

C. 32

D. 36

E. 40

* A solution will be posted in two days.

Its an old question but I found a slightly different way to approach it than the listed methods.

In the first mixture, Peanuts are 3/4 and consequently cashews are 1/4. Their ratio:

\(\frac{c}{p} = \frac{1}{3}\)

\(c = \frac{p}{3}\)

In mixture 2:

\(\frac{c}{p-8} = \frac{3}{7}\)

\(7c = 3(p-8)\)

from the first mixture equation, we know \(c = \frac{p}{3}\)

\(7*\frac{p}{3} = 9p - 72\)

simplifying

\(72 = 9p - 7p\)

\(2p = 72\)

\(p = 36\)

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