SOLUTION: A chemist needs 110 milliliters of a 80% solution but has only 76% and 98% solutions available, find out how many milliliters of each that should be mixed to get the desired soluti

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Question 1115451: A chemist needs 110 milliliters of a 80% solution but has only 76% and 98% solutions available, find out how many milliliters of each that should be mixed to get the desired solution
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
component percent ---------------- quantity
Solution I 0.76 ---------------- x ml
Solution II 0.98 ---------------- 110 - x ml
Mixture 0.50 ---------------- 110

0.76 x + 0.98 ( 110 - x ) = 110.00 * 0.80

0.76 x + 107.8 - 0.98 x = 88.00
0.76 x - 0.98 x = 88 - 107.8
-0.22 x = -19.8
/ -0.22
x = 90 ml 76.00% Solution I
20 ml 98.00% Solution II

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
ONE VARIABLE METHOD 
                  VOLUME        PURE SOLUTE

76% SOLUTION        x            76x

98% SOLUTION       110-x         98(110-x)

TARGET 80%         110         76x+98(110-x)

76x%2B98%28110-x%29=80%2A110
Solve for x and evaluate 110-x.


TWO VARIABLE METHOD
                  VOLUME        PURE SOLUTE

76% SOLUTION        x            76x

98% SOLUTION       y             98y

TARGET 80%         110         76x+98y

system%28x%2By=110%2C76x%2B98y=80%2A110%29
Simplify the pure-solute equation and solve the system with either substitution method or elimination method.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a way to solve mixture problems like this involving two ingredients that is much easier to use than the traditional algebraic method shown by the other tutors.

The ratio in which the two ingredients must be mixed is exactly determined by where the percentage of the final mixture lies between the percentages of the two ingredients.

For your problem....

80-76 = 4; 98-80 = 18.

The ingredients must be mixed in the ratio 4:18, or 2:9. With 110 ml in the final mixture, that means 20ml of one ingredient and 90ml of the other.

Since the percentage of the final mixture is closer to 76% than to 98%, the larger part must be the 76% ingredient.

Answer: 90ml of 76%; 20ml of 98%