SOLUTION: A chemist needs 80 milliliters of a 60% solution but she only has 58% and 66% solutions available. Calculate how many milliliters of each should be mixed to get the desired result.

Question 1121852: A chemist needs 80 milliliters of a 60% solution but she only has 58% and 66% solutions available. Calculate how many milliliters of each should be mixed to get the desired result. How many milliliters of the 58% solution should she use?
She should use _______
milliliters of 58% solution.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x of 58%
80-x of 66%
80*60, to represent pure solute

Simplify and solve...
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the number of ml of the 58% solution (what the problem asks us to find).
Then (80-x) is the number of ml of the 66% solution.

Write and solve the equation that says the sum of the amounts of actual chemical in the two ingredients is equal to the amount in the mixture. To make it clear what the equation means, write each term as (percentage) times (amount).

You can do the algebra to solve the problem by that method.

However, here is a method that I find far easier and much faster for solving problems like this.

(1) The target percentage of 60% is 3 times as close to 58% as it is to 66%: 60%-58% = 2%; 66%-60% = 6%.
(2) That means the mixture has to contain 3 times as much of the 58% solution as the 66% solution.
(3) 80 ml mixed in the ratio 3:1 means 60 ml of the 58% solution and 20 ml of the 66% solution.

Answer: 60 ml of the 58% solution.
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