Question

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Amy mixes 12 liters of 26% acid solution with a 40% acid solution to make a 33% acid solution.How many liters of 40% solution did she use
A.36 liters
B. 12 liters
C. 16 liters
D.4.8 liters
Amy mixes 12 liters of 16% acid solution with a 40% acid solution to make a 32% acid solution.How many liters of 40% solution did she use?
A. 36 liters
B. 24 liters
C. 16 liters
D. 4.8 liters
Marie mixes 16 liters of 18% acid solution with a 27% acid solution to make a 21% acid solution.How many liters of 27% solution did she use?
A.8 liters
B. 12 liters
C.13.7 liters
D.16 liters

Answer 1

1.
12 liters of 26% acid solution contain
`26\% * 12=0.26 * 12=3.12` liters of acid.
x liters of 40% acid solution contain
`40\%x=0.4x` liters of acid.
The third solution is made from the two mixed solution so its volume is
`12+x`, and the volume of acid in it is
`0.4x+3.12`. Its concentration is 33% or 0.33.
The concentration of a solution is the volume of the solution divide by the volume of acid in it.


`(0.4x+3.12)/(12+x)=0.33 \\ 0.4x+3.12=0.33(12+x) \\ 0.4x+3.12=3.96+0.33x \\ 0.07x=0.84 \\ x=12`

The answer is B.

2.
12 liters of 16% acid solution contain
`16\% * 12=0.16 * 12=1.92` liters of acid.
x liters of 40% acid solution contain
`40\%x=0.4x` liters of acid.
The volume of the third solution is
`12+x`, and the volume of acid in it is
`0.4x+1.92`. Its concentration is 32% or 0.32.


`(0.4x+1.92)/(12+x)=0.32 \\ 0.4x+1.92=0.32(12+x) \\ 0.4x+1.92=3.84+0.32x \\ 0.08x=1.92 \\ x=24`

The answer is B.

3.
16 liters of 18% acidsolution contain
`18\% * 16=0.18 * 16=2.88` liters of acid.
x liters of 27% acid solution contain
`27\%x=0.27x` liters of acid.
The volume of the third solution is
`16+x`, and the volume of acid in it is
`0.27x+2.88`. Its concentration is 21% or 0.21.


`(0.27x+2.88)/(16+x)=0.21 \\ 0.27x+2.88=0.21(16+x) \\ 0.27x+2.88=3.36+0.21x \\ 0.06x=0.48 \\ x=8`

The answer is A.