A pharmacist wants to mix two solutions to obtain 100 cc of a solution that has an 8% concentration of a certain medicine. If one solution has a 10% concentration of the medicine and the second has a 5% concentration, how much of each of these solutions should she mix?

Question
Equations and inequalities
asked 2020-10-28
A pharmacist wants to mix two solutions to obtain 100 cc of a solution that has an 8% concentration of a certain medicine. If one solution has a 10% concentration of the medicine and the second has a 5% concentration, how much of each of these solutions should she mix?

Answers (1)

2020-10-29
Let x be the amount of 10% concentracion so that 100-x is the amount of 5% concentracion, both in cc.
In terms of percentage, we write:
0.10(x)+0.05(100-x)=0.08(100)
Solve for x: 0.10x+5-0.05x=8
0.05x+5=8
0.05x=3
\(\displaystyle{x}=\frac{{3}}{{0.05}}\)
x=60
Hence, the pharmacist needs 60 cc of the 10% concentracion and 40 cc of the 5% concentracion.
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