Question

How many quarts of a 50% acid solution must be added to 20 quarts of a 20% acid

solution to obtain a 40% acid solution?

Answer 1

Explanation:

while the other answer is correct, let me try to explain this in a different optical way :

50% means 50/100 = 1/2 = 5/10 of the substance is acid.

20% means 20/100 = 1/5 = 2/10 of the substance is acid.

40% means 40/100 = 2/5 = 4/10 of the substance is acid.

now, we want to find the quantity of x quarts that satisfies the desired balance :

x × 50% + 20 × 20% = (x + 20) × 40%

x × 5/10 + 20 × 2/10 = (x + 20) × 4/10

5x/10 + 4 = 4x/10 + 8

x/10 = 4

x = 40

so, yes, we need to add 40 quarts of the 50% solution.

that gives us 60 quarts, with 40% = 40/100 = 4/10 = 2/5 = being acid : 60 × 2/5 = 120/5 = 24 quarts

Answer 2

40 quarts

Explanation:

The amount of additional 50% acid solution can be found by writing an equation for the amount of acid in the mix.

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Let x represent the number of quarts of 50% acid solution that need to be added. The total number of quarts of acid in the 40% mix is ...

0.50x +0.20(20) = 0.40(x +20)

0.10x = 0.20(20) . . . . . . . subtract 0.40x +0.20(20)

x = 40 . . . . . . . . . . . . divide by 0.10

40 quarts of 50% solution must be added.

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Additional comment

That will make a total of 60 quarts of solution, of which 24 quarts (40%) are acid.