a chemist needs 120 milliliters of a 72% solution but has only 51% and 87% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

The chemist needs 50 mL of 51% solution and 70 mL of 87% solution.

Step-by-step explanation:

If x is the volume of 51% solution, and y is the volume of 87% solution, then:

x + y = 120

0.51x + 0.87y = 0.72 (120)

Solve the system of equations.

0.51x + 0.87 (120 - x) = 0.72 (120)

0.51x + 104.4 - 0.87x = 86.4

0.36x = 18

x = 50

y = 70

The chemist needs 50 mL of 51% solution and 70 mL of 87% solution.