Bunuel wrote:
A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?
A. 200
B. 400
C. 500
D. 600
E. 800
Kudos for a correct solution.
We can solve this question with the
weighted averages formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...Let x = the number of units of 12% phosphoric acid solution needed
Since we're adding x units to 400 units, the volume of the RESULTING mixture =
400 + X A scientist has 400 units of a 6% phosphoric acid solution. . . So, the PROPORTION of 6% solution in the RESULTING mixture =
400/(400 + x). . . and an unlimited supply of 12% phosphoric acid solutionWe are adding x units of 12% solution
So, the PROPORTION of 12% solution in the RESULTING mixture =
x/(400 + x)How many units of the latter must she add to the former to produce a 10% phosphoric acid solution? We want the resulting mixture to contain 10% phosphoric acid
Applying the formula, we can write: 10 =
[400/(400 + x)][6] +
[x/(400 + x)][12]Multiply both sides by (400 + x) to get: 10(400 + x) = 2400 + 12x
Expand left side to get: 4000 + 10x = 2400 + 12x
Solve: x = 800
Answer: E
Cheers,
Brent
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