Problem Solving

The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity as the first mixture has cashews 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.

Max@Math Revolution wrote:The first mixture consists of its 3/4 is peanuts and the rest is cashews. The second mixture has the same quantity as the first mixture has cashews 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

We can PLUG IN THE ANSWERS, which represent the weight of the peanuts in the first mixture.

Since 3/4 of the first mixture is peanuts, P:C = 3:1, implying that the weight of the peanuts must be a MULTIPLE OF 3.
Eliminate B, C and E.

When the correct value for P is plugged in, removing 8 pounds of peanuts will yield for the second mixture the following ratio:
(New P) : C = 7:3.

D: 36 pounds
Since P:C = 3:1 = 36:12, the first mixture is composed of P=36 and C=12.
After 8 pounds of peanuts are removed, we get:
(New P) : C = (36-8):12 = 28:12 = 7:3.
Success!

The correct answer is D.

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

This is frequently given on GMAT MATH, which is "2 by 2" question.



On the table above, 3f-8:f=7:3 -> 3(3f-8)=7f, 9f-24=7f, f=12. Hence, in the first mixture, peanuts=3f=3(12)=36 is the answer. Therefore, D is the answer.