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.
