Question

You need 550 mL of a 50% alcohol solution. On hand, you have a 55% alcohol mixture. How much of the 55% alcohol mixture and pure water will you need to obtain the desired solution?

Answer 1

We need 500 ml of alcohol mixture and 50 ml of water.

Explanation:

The 50% concentration of the final solution is a result of mixing the 55% concentration with water, which is 0% concentration. Multiply the concentration of each liquid times the # of ml you will use, add these and divide by the total ml to get 50%

x = the number of ml of the 55% alcohol mixture

y = the number of ml of water

x + y = 550

`\frac{{0.55 x + (0) y }}{550} =0.50`

Again, the 0 above represents the water which is 0% concentration

`(0.55 x)/(550)` = 0.50

0.55 x = 275

x =
`(275)/(0.55)` = 500

plug 500 into the equation x + y = 550

500 + y = 550

y = 50

Use 500 ml of the 55% solution and 50 ml of water.