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Peter combines two different types of trail mix, A and B, to make 400

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Bunuel
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Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  15 Aug 2017, 01:08
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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?

A. 80
B. 160
C. 240
D. 320
E. 360
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  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)
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  15 Aug 2017, 02:22
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0.1x+0.2(400-x)=38
80-38 =0.1x
320=x
D is the answer
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  15 Aug 2017, 02:23
prachi18oct wrote:
0.1x+0.2(400-x)=38
80-38 =0.1x
320=x
D is the answer

It's not 38 but 48.
Still the method is alright.
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  15 Aug 2017, 02:29
10/100 * A + 20/100 * B = 48 ----------------1
A+B = 400----------------------------2
solving 1 and 2 will give
A= 320
B = 80.
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  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
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  16 Aug 2017, 00:54
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  17 Aug 2017, 06:37
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let raisin in mix 1 is x that is used
let raisin in mix 2 is y that is used

mix 1 is 10% and mix 2 is 20% and blend is 48/400 *100 = 12%

so 10x +20y / (x+y) = 12
x=4y
x+y= 400
x=320 answer D
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  18 Aug 2017, 09:13
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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


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
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Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  18 Aug 2017, 12:50
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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

10x = 400
x = 40
A = 8x = (8)(40) = 320

Answer D
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  20 Aug 2017, 02:06
Let total Weight of Trail A is 'a' and of Trail B is 'b'.

According to statement:

Equation for Raisins weight:
0.1a + 0.2b = 48 ----- eqn 1

Equation for Total weight:
a + b = 400 ----- eqn 2

Solving both equation, we get
a= 320 & b= 80.

Hence, Ans D
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  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.

Hence the answer is D.
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  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%

(A/(400-A)) = (20-12)/(12-10)
A=320
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Re: Peter combines two different types of trail mix, A and B, to make 400 [#permalink] New post  29 Jan 2020, 02:14
1st approach:
48 is 12% of 400;
A/B = (20 - 12)/(12-2) = 4/1;
400*4/5 = 320

2nd approach:
10A + 20B = 12(A + B) = 12A + 12B;
8B = 2A => 4B = A;
A/B = 4/1
400*4/5 = 320
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