Alcohol mixture problem

Question

You need 975 mL of a 25% alcohol solution. On hand, you have a 65% alcohol mixture. How much of the 65% alcohol mixture and pure water will you need to obtain the desired solution?

Answer 1

Let a be the amount of the 65% alcohol solution and w be the amount of pure water to add.

0.65a + 0w = 0.25(975) (Zero is multiplied by the amount of water since there is no alcohol content)

a+w = 975

There are two simultaneous equations and two variables so you can solve for both a and w.

a = (0.25/0.65)(975)

w = 975-a

If you solve for a and w you should get the same answer as Mark's solution using a different approach.

Answer 2

Because pure water is added the solutions must be in terms of water.

975 mL of 75% water solution is the result

You have a 35% water solution

w represents the amount pure water

0.35(975 - w) + w = 0.75(975)

Can you solve for w and answer?