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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?

Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink]

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15 Aug 2017, 02:06

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48 ounces in 400 ounces is \(\frac{48}{400}*100 = 12\)%

We have two trails - Mix A and Mix B containing 10% and 20% of raisins respectively. Therefore,

Mix A---------------Mix B |10|-----------------|20| ----------|12|----------- |8|-------------------|2|

Hence, they have to mixed in the ratio 4:1(Mix A:Mix B)

Therefore, we will need \(\frac{4}{5}*400\) of the trail mix being prepared to come from Mix A, thereby making the total weight in ounces of Mix A, 320 ounces(Option D) _________________

Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink]

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15 Aug 2017, 21:11

Bunuel 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

.1A+.2B=.12(A+B) A/B=4/1 4/5*400=320 ounces of mix A D

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

We can let a = the amount of trail mix A and b = the amount of trail mix B. We have two equations:

a + b = 400

b = 400 - a

and

0.1a + 0.2b = 48

a + 2b = 480

Substituting b = 400 - a in a + 2b = 480, we have:

a + 2(400 - a) = 480

a + 800 - 2a = 480

320 = a

Answer: D
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Peter combines two different types of trail mix, A and B, to make 400 [#permalink]

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18 Aug 2017, 12:50

Bunuel 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

\(\frac{48}{400}\) = 12 percent raisins in mix of A + B

Change decimal percentages to integers to make calculation easier

10A + 20B = 12(A + B)

8B = 2A

\(\frac{A}{B}\) = \(\frac{8x}{2x}\) --> 10x parts total

Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink]

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20 Aug 2017, 06:12

Bunuel 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

1. A + B = 400 ounces. 2. 0.1A + 0.2B = 48 ~ A + 2B = 480. 3. Solve two equation, got B = 80 and A = 320.

Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink]

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20 Aug 2017, 07:33

Bunuel 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

Using allegation :

Assume: Weight of A = A Weight of B = B Conc. of A = 10% Conc. of B = 20% Avg. Conc. of mix. = (48/400)*100 = 12%