Question 1162996: You need a 20% acid solution. You have 980 mL of 15% on hand. How much of a 90% acid solution should you add to obtain the desired solution? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52864) (Show Source):
The base equation is
0.9*x + 0.15*980 = 0.2*(x+980).
It states that the amounts of the pure acid in ingredients (left side)
sum up to the amount of the pure acid in resulting mixture (right side).
From the equation,
x = = 70 mL.
ANSWER. 70 mL of the 90% acid solution to add.
Here is an alternative to the standard algebraic solution method shown by the other tutor.
The 20% target is much closer to the 15% of the original solution than it is to the 90% of the solution that is being added. So the amount of 90% acid being added should be very small compared to the 980mL of the original solution.
Specifically, 20% is only 1/15 of the way from 15% to 90%. (15 to 90 is a difference of 75; 15 to 20 is a difference of 5; 5/75 = 1/15.)
That means 1/15 of the final mixture should be the 90% acid that is being added.
So the 980mL of the original 15% acid is 14/15 of the final mixture; that makes 1/15 of the final mixture 980/14 = 70mL.
