Mixture Problem

Question

A chemist needs 160 milliliters of a 50% solution but has only 30% and 62% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. 

Answer 1

Hi Alexis,

We obtain the following information from the mixture problem:

(160mL)(0.50)= Desired Solution

(160mL-X)(0.30) = amount on 30% Solution

(160mL-Y)(0.62) = amount on 62% Solution

(160mL-(160mL-X))(0.62) = amount on 62% Solution (Expressed in terms of X)

The total of X + Y = 160mL.

Now we can express the mixture problem as an equation:

(160mL)(0.50) = (160mL-X)(0.30) + (160mL-(160mL-X))(0.62)

(160mL)(0.50) = (160mL-X)(0.30) + (160mL-160mL+X)(0.62)

(160mL)(0.50) = (160mL-X)(0.30) + (X)(0.62)

80mL = 48mL - 0.30X + 0.62X

80mL = 48mL + 0.32X

32mL = 0.32X

100mL = X