Salad dressing \(A\) is made up of 30% vinegar and 70% oil, and salad dressing \(B\) contains 10% vinegar and 90% oil. If the 2 dressing are combined to produce a salad dressing that is 15% vinegar, dressing \(A\) comprises what % of the new dressing?
A. 15%
B. 20%
C. 25%
D. 40%
E. 55%
[spoiler]OA=C[/spoiler]
Source: Princeton Review
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Salad dressing \(A\) is made up of 30% vinegar and 70% oil, and salad dressing \(B\) contains 10% vinegar and 90% oil.
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Solution:VJesus12 wrote: ↑Wed May 20, 2020 6:11 amSalad dressing \(A\) is made up of 30% vinegar and 70% oil, and salad dressing \(B\) contains 10% vinegar and 90% oil. If the 2 dressing are combined to produce a salad dressing that is 15% vinegar, dressing \(A\) comprises what % of the new dressing?
A. 15%
B. 20%
C. 25%
D. 40%
E. 55%
[spoiler]OA=C[/spoiler]
We can let the amount of dressing A = a and the amount of dressing B = b, thus:
0.3a + 0.1b = 0.15(a + b)
30a + 10b = 15a + 15b
15a = 5b
3a = b
The total amount of the new salad dressing is a + b. Thus, dressing A is a/(a + b) = a/(a + 3a) = 1/4 = 25% of the new dressing.
Answer: C
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