A scientist has \(400\) units of a \(6\%\) phosphoric acid solution and an unlimited supply of \(12\%\) phosphoric acid

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