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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

Sagot :

naǫ
1.
12 liters of 26% acid solution contain [tex]26\% \times 12=0.26 \times 12=3.12[/tex] liters of acid.
x liters of 40% acid solution contain [tex]40\%x=0.4x[/tex] liters of acid.
The third solution is made from the two mixed solution so its volume is [tex]12+x[/tex], and the volume of acid in it is [tex]0.4x+3.12[/tex]. 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.

[tex]\frac{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[/tex]

The answer is B.

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

[tex]\frac{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[/tex]

The answer is B.

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

[tex]\frac{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[/tex]

The answer is A.

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