## Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a

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### Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a

by BTGmoderatorDC » Tue Aug 24, 2021 8:54 pm

00:00

A

B

C

D

E

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Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0

OA C

Source: Princeton Review

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### Re: Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a

by swerve » Fri Aug 27, 2021 4:24 pm
BTGmoderatorDC wrote:
Tue Aug 24, 2021 8:54 pm
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0

OA C

Source: Princeton Review
$$x+y = 4 \quad (1)$$ volume equation

$$0.15x+0.5y = 0.3*4 \quad (2)$$ concentrate equation

Solving $$(1) \& (2):$$
$$0.15x+0.5y= 1.2$$
$$15x+50y=120$$

From $$(1)$$ we get, $$y=4-x,$$ thus
$$15x+50(4-x) =120$$
$$15x+200-50x=120$$
$$35x = 80$$
$$x= \dfrac{80}{35} = \dfrac{16}{7} = 2.28 \Rightarrow$$ C

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