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

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

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We can solve this question with the weighted averages formula:VJesus12 wrote: ↑Thu Sep 16, 2021 11:11 amA 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

**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