10. A chemist needs to mix an 18% acid solution with a 45% acid solution to obtain 12 liters of 36% solution. How many liters of each of the acid solutions must be used?

Question

asked Mar 21, 2023 9.8k views

1 Answer

Willem · Answer 1 · 2023-03-26T07:31:31+0000

Answers:

4 liters of the 18% acid

8 liters of the 45% acid

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Step-by-step explanation:

Let's call the bottles A and B

x = amount, in liters, of bottle A used

12-x = amount, in liters, of bottle B used

Bottle A has 0.18x liters of pure acid

Bottle B has 0.45(12-x) liters of pure acid

These amounts must add to 0.36*12 = 4.32 liters of pure acid since we want 12 liters of a 36% solution.

So,

0.18x + 0.45(12-x) = 4.32

0.18x + 0.45(12)+0.45(-x) = 4.32

0.18x + 5.4-0.45x = 4.32

-0.27x + 5.4 = 4.32

-0.27x = 4.32 - 5.4

-0.27x = -1.08

x = (-1.08)/(-0.27)

x = 4 liters which is the amount of bottle A needed

12-x = 12-4 = 8 liters is the amount of bottle B needed

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Check:

Using 4 liters of bottle A means we contribute 4*0.18 = 0.72 liters of pure acid from this bottle alone.

Using 8 liters from bottle B adds another 8*0.45 = 3.6 liters of pure acid

Then, 0.72+3.6 = 4.32 which matches with the 4.32 mentioned earlier. Therefore, the answer is fully confirmed.