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

[BTGmoderatorDC]

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

[swerve]

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