VJesus12 wrote: ↑Thu Sep 16, 2021 11:11 am
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
Answer:
E
Source: Magoosh
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 solution
We 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
