Question

How many liters of 10% acid solution should be mixed with 30 liters of a 50% acid solution to get a mix that a 20% acid?

Answer 1

The attached diagram shows the QUANTITIES and concentrations of each container. The first container has x liters in it ("how many liters of 10%..."). The second container has 30 liters (and 50% of that is acid). The third container has x + 30 liters (because you dumped the first two containers into the third container), and 20% of that is acid.

Write an equation that shows how the acid adds up:

10% of x plus 50% of 30 equals 20% of (x + 30).

$.10x+.50(30)=.20(x+30) \\ .10x+15=.20x+6 \\ 15=.10x+6 \\ 9=.10x \\ 90=x$

You should add 90 liters of the 10% solution.

Answer 2

90 liters of 10% acid solution should be mixed with 30 liters of a 50% acid solution to get a mix that is 20% acid

An equation is used to show the relationship between two or more variables and numbers.

Let x represent the amount of acid solution in liters. Hence:

(x * 10%) + (30 * 50%) = (x + 30) * 20%

0.1x + 15 = 0.2x + 6

0.1x = 9

x = 90 liters

90 liters of 10% acid solution should be mixed with 30 liters of a 50% acid solution to get a mix that is 20% acid

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