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Weighted Averages - 2 mixtures

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by gmattesttaker2 » Fri Feb 21, 2014 11:40 pm
Hello,

Can you please tell me how to solve this:

By weight liquid A makes up 7.0 percent of solution I and 14.5 percent of solution II. If 3 grams of solution I is mixed with 2 grams of solution II then liquid A accounts for what percent of the weight of the resulting solution?

A) 6.09%
B) 10%
C) 10.75%
D) 21.5%
E) 50%

OA: B


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by theCodeToGMAT » Sat Feb 22, 2014 2:58 am
Let sol I = 100g ... So, A = 7g
Let sol II = 100g ... So, A = 14.5g

3g of I => 3 * 7/100 of A = .21g
2g of II=> 2 * 14.5/100 of A = .29g

Total A = .50g
Percentage = 0.50/5 * 100 = 10%

[spoiler]{B}[/spoiler]
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by GMATGuruNY » Sat Feb 22, 2014 3:12 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve this:

By weight liquid A makes up 7.0 percent of solution I and 14.5 percent of solution II. If 3 grams of solution I is mixed with 2 grams of solution II then liquid A accounts for what percent of the weight of the resulting solution?

A) 6.09%
B) 10%
C) 10.75%
D) 21.5%
E) 50%
3 grams of a 7% solution are combined with 2 grams of a 14.5% solution to form a mixture of 5 grams.
Average percentage for the 5 grams = (3*7 + 2*14.5)/5 = 50/5 = 10%.

The correct answer is B.
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by Brent@GMATPrepNow » Sat Feb 22, 2014 7:30 am
gmattesttaker2 wrote:
By weight liquid A makes up 7.0 percent of solution I and 14.5 percent of solution II. If 3 grams of solution I is mixed with 2 grams of solution II then liquid A accounts for what percent of the weight of the resulting solution?

A) 6.09%
B) 10%
C) 10.75%
D) 21.5%
E) 50%
We can also use the weighted averages formula:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

We have 3 grams of solution I and 2 grams of solution II for a TOTAL of 5 grams.

So,
Solution I comprises 3/5 of the combined mixture and contains 7% liquid A
Solution II comprises 2/5 of the combined mixture and contains 14.5% liquid A

By the formula, Average of combined solutions = (3/5)(7) + (2/5)(14.5)
= 21/5 + 29/5
= 50/5
= 10
= B

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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