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Joined: 10 Apr 2015
Posts: 6218
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Two mixtures A and B contain milk and water in the ratios 2:
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04 Dec 2020, 07:03
04 Dec 2020, 07:03
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Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?
A. 144
B. 122.5
C. 105.10
D. 72
E. 134
A. 144
B. 122.5
C. 105.10
D. 72
E. 134
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Two mixtures A and B contain milk and water in the ratios 2:
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04 Dec 2020, 07:04
04 Dec 2020, 07:04
1
GreenlightTestPrep wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?
A. 144
B. 122.5
C. 105.10
D. 72
E. 134
A. 144
B. 122.5
C. 105.10
D. 72
E. 134
When solving some mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.
First recognize that if mixture A has a milk to water ratio of 2:5, then the mixture is 2/7 milk.
Also recognize that if mixture B has a milk to water ratio of 5:4, then the mixture is 5/9 milk.
Start with 90 gallons of mixture B, which is 5/9 milk:
When we draw this with the ingredients separated, we see we have 50 gallons of milk in the mixture.
Next, we'll let x = the number of gallons of mixture A we need to add.
Since 2/7 of mixture A is milk, we know that (2/7)x = the volume of MILK in this mixture:
At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:
Since the RESULTING mixture is 40% milk (i.e., 40/100 of the mixture is milk), we can write the following equation:
[50 + (2/7)x]/(90 + x) = 40/100
Simplify to get: [50 + (2/7)x]/(90 + x) = 2/5
Cross multiply to get: 5[50 + (2/7)x] = 2(90 + x)
Expand: 250 + (10/7)x = 180 + 2x
Subtract 180 from both sides to get: 70 + (10/7)x = 2x
Multiply both sides by 7 to get: 490 + 10x = 14x
Rearrange: 490 = 4x
Solve: x = 490/4 = 245/2 = 122.5
Answer: B
RELATED VIDEO
Re: Two mixtures A and B contain milk and water in the ratios 2:
[#permalink]
02 Feb 2021, 10:23
02 Feb 2021, 10:23
1
Hi, I am not sure if this can be done using weighted average technique :
So, milk % in A = 2/7 = 28%
So, milk % in B = 5/9 = 55%
Result mixture milk % = 40%
thus, using technique :
28 55
- -
40
= =
15 12
thus, 15/12 = x/90
x = 112.5 (Ans is 122.5)
Hope you can help
So, milk % in A = 2/7 = 28%
So, milk % in B = 5/9 = 55%
Result mixture milk % = 40%
thus, using technique :
28 55
- -
40
= =
15 12
thus, 15/12 = x/90
x = 112.5 (Ans is 122.5)
Hope you can help
