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A scientist has 400 units of a 6% phosphoric acid solution, and an unl
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16 Sep 2021, 09:39
16 Sep 2021, 09:39
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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
A. 200
B. 400
C. 500
D. 600
E. 800
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Re: A scientist has 400 units of a 6% phosphoric acid solution, and an unl
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16 Sep 2021, 10:06
16 Sep 2021, 10:06
1
Carcass 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
A. 200
B. 400
C. 500
D. 600
E. 800
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
RELATED VIDEO
A scientist has 400 units of a 6% phosphoric acid solution, and an unl
[#permalink]
16 Sep 2021, 22:09
16 Sep 2021, 22:09
1
A : 6% phosphoric acid solution
B: 12% phosphoric acid solution
C: Resultant Solution = 10% phosphoric acid solution
So the ratio in which we will mix A and B to Form C is
12-10:10-6
=> 2:4
=>1:2
thus we will take 1 parts of solution A and Add 2 parts of Solution B to form the desired solution C
as 1 part of A is equal to 400 units hence 2 parts of B will be required which is 2*400=800 units hence option(E)
B: 12% phosphoric acid solution
C: Resultant Solution = 10% phosphoric acid solution
So the ratio in which we will mix A and B to Form C is
12-10:10-6
=> 2:4
=>1:2
thus we will take 1 parts of solution A and Add 2 parts of Solution B to form the desired solution C
as 1 part of A is equal to 400 units hence 2 parts of B will be required which is 2*400=800 units hence option(E)
