Peter combines two different . . .

Vincen wrote:Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. How many ounces of trail mix A does Peter use to make his mix?

A) 80
B) 160
C) 240
D) 320
E) 360

The OA is D.

The calculus I did gave as the result 360. It seems I did something wrong. Experts, please help me.

Say the weight of trail mix A = a, and the weight of trail mix B = b

Thus, we have a + b = 400 ---(1)

Also, the weight of raising by mix A = 10% of a = a/10; and
the weight of raising by mix B = 20% of b = b/5

Thus, a/10 + b/5 = 48

a + 2b = 480---(2)

Upon solving (1) and (2), we get a = 320 ounces.

The correct answer: D

Hope this helps!

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Hi Vincen,

We're told that Peter combines two different types of trail mix, A and B, to make 400 ounces of his own mix, which includes 48 ounces of raisins. Trail mix A is 10% raisins by weight, and Trail mix B is 20% raisins by weight. We're asked for the number of ounces of trail mix A Peter uses to make his mix. This question can be approached in a number of ways; here's how you can solve it with some basic arithmetic and TESTing THE ANSWERS:

To start, we need to know what PERCENTAGE of the overall mixture is raisins. 48/400 = 24/200 = 12/100 = 12%. Since Mix A is 10% raisins and Mix B is 20% raisins, we will clearly have a LOT MORE of Mix A than Mix B (If we had an equal amount of each, then the overall mixture would be (10+20)/2 = 15% raisins). Thus, the correct answer must be a LOT GREATER than 200.

Let's TEST Answer D: 320 ounces of Mix A... meaning that there would also be 80 ounces of Mix B

Mix A: (.1)(320) = 32 ounces of raisins
Mix B: (.2)(80) = 16 hours of raisins
Total raisins = 32 + 16 = 48 ounces
This is an exact MATCH for what we were told, so this MUST be the answer!

Final Answer: D

GMAT assassins aren't born, they're made,
Rich