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

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

by VJesus12 » Thu Sep 16, 2021 11:11 am

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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

Source: Magoosh

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### Re: A scientist has $$400$$ units of a $$6\%$$ phosphoric acid solution and an unlimited supply of $$12\%$$ phosphoric a

by [email protected] » Thu Sep 16, 2021 3:22 pm
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

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)] + [x/(400 + x)]
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