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
ANSWERED
asked 2021-05-30
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?

Expert Answers (2)

2021-06-01
36
 
Best answer
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.

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