1.
12 liters of 26% acid solution contain \(26\% \times 12=0.26 \times 12=3.12\) 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.
\(\frac{0.4x+3.12}{12+x}=0.33 \\ 0.4x+3.12=0.33(12+x) \\ 0.4x+3.12=3.96+0.33x \\
0.07x=0.84 \\
x=12\)
The answer is B.
2.
12 liters of 16% acid solution contain \(16\% \times 12=0.16 \times 12=1.92\) 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.
\(\frac{0.4x+1.92}{12+x}=0.32 \\
0.4x+1.92=0.32(12+x) \\
0.4x+1.92=3.84+0.32x \\
0.08x=1.92 \\
x=24\)
The answer is B.
3.
16 liters of 18% acidsolution contain \(18\% \times 16=0.18 \times 16=2.88\) 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.
\(\frac{0.27x+2.88}{16+x}=0.21 \\
0.27x+2.88=0.21(16+x) \\
0.27x+2.88=3.36+0.21x \\
0.06x=0.48 \\
x=8\)
The answer is A.
