SOLUTION: An industrialist has 450 litres of a chemical which is 70% pure. he mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% . pure. find the

Question 1101892: An industrialist has 450 litres of a chemical which is 70% pure. he mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% . pure. find the amount of the 90% pure chemical used.
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52872)   (Show Source): You can put this solution on YOUR website!
.
an industrialist has 450 litres of a chemical which is 70% pure. he mixes it with a chemical of the same type but 90% pure
so as to obtain a mixture which is 75% . pure. find the amount of the 90% pure chemical used.
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Let x be the volume of the 90% solution, in liters. 450 liters of the 70% solution contain 0.7*450 liters of the pure. x liters of the 90% solution contain 0.9*x liters of the pure. Final (450+x) liters solution contain 0.75*(450+x) liters of the pure. PURE + PURE = PURE ========================> 0.7*450 + 0.9*x = 0.75*(450+x) You just got your balance equation for "the pure". Now solve it: 0.7*450 + 0.9x = 0.75*450 + 0.75x ====> 0.9x - 0.75x = 0.75*450 - 0.7*450, 0.15x = 0.05*450 ====> x = = 150. Answer. 150 liters of the 90% solution should be added. Check. There are 0.7*450 + 0.9*150 = 450 liters of the pure in the input components. There are 0.75*(450+150) = 450 liters of the pure in the FINAL solution. ! Correct !

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Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
An industrialist has 450 litres of a chemical which is 70% pure. He mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% . pure. Find the amount of the 90% pure chemical used.

The industrialist has no pure chemical as far as we know.
He has on hand a mixture which is 70% and a mix that is 90% and wants to blend them to get a mix that is 75%
Pure means 100%
The 70% mix is a blend of 30%*450 = 125 L something else and 70 %*450 =315 L pure
Otherwise, the math presented is correct.
We have on hand 450 L of 70% solution.
Using the method of alligation.

90 5 5/15*450=150 L of 90% solution 75 600 L of 75% solution 70 15 450 L of 70% solution 20

check
0.9 * 150 + 0.7 * 450 = 0.75*(450+150)
135.0 + 315.0 = 0.75*(600)
450.0 = 450.0
ok

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