Question

# A chemist needs 150 milliliters of a 54% solution but has only 10% and 70% solutions available. How many milliliters of each should be mixed to get th

Upper level algebra
A chemist needs 150 milliliters of a 54% solution but has only 10% and 70% solutions available. How many milliliters of each should be mixed to get the desired solution?

2021-06-01
2021-08-04

If x is the amount of 10% solution, then $$\displaystyle{150}−{x}$$ is the amount of 70% solution.
In terms of percentage, the desired solution must be 54%:
$$\displaystyle{0.10}{x}+{0.70}{\left({150}−{x}\right)}={0.54}{\left({150}\right)}$$
Solve for x:
$$\displaystyle{0.10}{x}+{105}−{0.70}{x}={81}$$
$$\displaystyle−{0.60}{x}+{105}={81}$$
$$\displaystyle−{0.60}{x}=−{24}$$
$$\displaystyle{x}={40}$$
So, the chemist needs 40 milliliters of 10% solution and 110 milliliters of 70% solution.