You need a 50% alcohol solution. On hand, you have a 500 mL of a 75% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

Question

You need a 50% alcohol solution. On hand, you have a 500 mL of a 75% alcohol mixture. How much pure water will you need to add to obtain the desired solution?

You will need

 _____ mL of pure water

to obtain

______ mL of the desired 50% solution.

Answer 1

50% is within 25 of 75

and within 50 of 0

you need 50/25 = 2 = twice as much 75 as pure water

500 = 2(250)

500(.75) + x(0) = (500+x).50

375 = 250 +.5x

.5x = 375-250 = 125

x = 125/.5 = 250 mL of pure water