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Sagot :
Let x, y, and z be the amounts (in liters) of the 15%, 35%, and 65% solutions, respectively.
The chemist wants to end up with 72 L of solution, so
x + y + z = 72
Now,
• x L of 15% solution contributes 0.15x L of acid
• y L of 35% solution contains 0.35y L of acid
• z L of 65% solution contains 0.65z L of acid
so that the total amount of acid in the resulting mixture is 45% of 72 L, or 32.4 L, which means
0.15x + 0.35y + 0.65z = 32.4
It's also stipulated that the chemist uses twice as much of the 65% solution as the 35% solution, which translates to
z = 2y
Substitute this into the other two equations:
x + 3y = 72
0.15x + 1.65y = 32.4
Solve for x in terms of y :
x = 72 - 3y
Solve for y :
0.15 (72 - 3y) + 1.65y = 32.4
10.8 - 0.45y + 1.65y = 32.4
1.2y = 21.6
y = 18
Solve for x and z :
x = 72 - 3 (18) = 18
z = 2 (18) = 36
So, the chemist should use
• 36 L of 65% solution (z)
• 18 L of 15% solution (x)
• 18 L of 35% solution (y)
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