A chemist has a bottle of 1% acid solution and a bottle of 5% acid solution. She wants to mix the two to get 100 mL of a 4% acid solution. How much of each should she use?

Answer 1

x = amount of 1% solution
y = amount of 5% solution

I organized the problem in a table:

SOLUTION AMOUNT TOTAL
1% solution -- x -- .01

5% solution -- y -- .05

4% solution --100-- 4

Now that you have this information, you create a system of equations:

.01x + .05y = 4

x + y = 100

I used the substitution method, by making the second equation equal to y first...

y = -x + 100

.01x + .05 (-x + 100) = 4

When you solve this, x = 25. So, you now know that 25 mL of the 1% solution is being used. Now, let's solve for y:

25 + y = 100

y = 75 mL

~~~~~Our final answer is that there are 25 mL of 1% solution and 75 mL of 5% solution.