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Sagot :
Answers:
4 liters of the 18% acid
8 liters of the 45% acid
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Explanation:
Let's call the bottles A and B
- Bottle A has 18% acid
- Bottle B has 45% acid
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.
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