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gracye
30.10.2020 •
Mathematics
You need 660 mL of a 80% alcohol solution. On hand, you have a 40% alcohol mixture. How much of the 40%
alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
mL of the 40% solution
and
mL of pure alcohol.
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Ответ:
Let a be the amount of 40% solution and b be the amount of pure alcohol that you will use.
You want to end up with a volume of 660 mL, so
a + b = 660
For each mL of solution used, the 40% solution would contribute 0.4 mL of alcohol, and the pure alcohol will contribute 1 mL of alcohol. In the desired solution, you want a concentration of 80% alcohol, so that it contains 0.8 • 660 mL = 528 mL of alcohol, and
0.4a + b = 528
Solve the system of equations above. Subtracting the second from the first eliminates b and lets us solve for a :
(a + b) - (0.4a + b) = 660 - 528
0.6a = 132
a = 220
Then
220 + b = 660
b = 440
So you will need 220 mL of the 40% solution and 440 mL of pure alcohol.
Ответ: