Solve the problem.
-A chemist needs 140 milliliters of a 70% solution but has only 66% and 94% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
A)123 ml of 66%; 17 ml of 94%
B)20 ml of 66%; 120 ml of 94%
C)120 ml of 66%; 20 ml of 94%
D)17 ml of 66%; 123 ml of 94%

Question

Quizplus · Accepted Answer

We can set up the equation:
0.66x + 0.94y = 0.7(140)
Solving for y, we get:
y = (0.7(140) - 0.66x)/0.94
We know that the total volume is 140 milliliters, so we can set up another equation:
x + y = 140
Solving for y, we get:
y = 140 - x
Substituting this into the first equation, we get:
(0.7(140) - 0.66x)/0.94 = 140 - x
Simplifying, we get:
x = 120
Substituting x = 120 into y = 140 - x, we get:
y = 20
Therefore, we need 120 milliliters of the 66% solution and 20 milliliters of the 94% solution. The answer is choice C. Let x be the amount of 66% solution needed, then 140-x will be the amount of 94% solution needed. 
0.66x + 0.94(140-x) = 0.7(140) 
0.94(140) - 0.28x = 98 
-0.28x = -18 
x = 64.29 (rounded to two decimal places) 
So we need 64.29 ml of 66% solution and 140-64.29=75.71 ml of 94% solution. 
These values are closest to the ones given in choice C: 120 ml of 66% and 20 ml of 94%.

Solve the Problem. -A Chemist Needs 140 Milliliters of a 70% Solution but 70