SOLUTION: Mixture A is 7.5% acid. To raise the concentration of acid to 10%, some pure acid will be added to the mixture. How many liters of mixture A and how many liters of pure acid are ne

Question 251464: Mixture A is 7.5% acid. To raise the concentration of acid to 10%, some pure acid will be added to the mixture. How many liters of mixture A and how many liters of pure acid are needed to end up with 200 liters of 10% solution.
Not sure if I started it out right, that's why I'm here!
x = pure acid
A = Mixture A
7.5 + x = (200)(.10) x = 12.5 liters
If that's right, I'm not sure where to go from there. If you can help me, that would be great! Thank you.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mixture A is 7.5% acid.

let x = amount of mixture A.

7.5% of x is equivalent to .075 * x (you have to divide percent by 100% to get proportion).

this means that .075 * x = amount of acid in mixture A.

let y = amount of mixture C.

then 1.0 * y = amount of acid in mixture B.

this is because 100% of mixture B is equivalent to 1.0 * mixture B.

mixture C is equal to 200 liters.

this means that:

x + y = 200

mixture C will contain 10% acid which means that mixture C will contain .10 * 200 = 20 liters of acid.

this means that:

.075 * x + y = 20

you have 2 equations that need to be solved simultaneously.

they are:

x + y = 200 (first equation)

.075*x + y = 20 (second equation)

you can solve for y in either equation and then solve for x in the other equation.

we'll solve for y in the first equation to get:

y = 200-x

we'll substitute for y in the second equation to get:

.075*x + (200-x) = 20

remove parentheses to get:

.075*x + 200 - x = 20

combine like terms to get:

-.925*x + 200 = 20

subtract 200 from both sides to get:

-.925*x = 20-100 = -180

divide both sides by -.925 to get:

x = -180 / -.925 = 194.5945946

use this value of x to solve for y in the first equation to get:

y = 200 - 194.5945946 = 5.405405405

use the values for x and y in the second equation to confirm that they are good.

the second equation is:

.075*x + y = 20

substituting for x and y in that equation, we get:

.075*194.5945946 + 5.405405405 = 20

this becomes 20 = 20 which is true confirming our values for x and y are good.

your answer is:

you need to add 5.405405405 liters of pure acid to make a 200 liter mixture of 10% acid.

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