I do not know how to do this

Question

You need 560 mL of a 65% alcohol solution. On hand, you have a 60% alcohol mixture. How much of the 60% alcohol mixture and pure alcohol will you need to obtain the desired solution?

Answer 1

Let x = mL of 60% solution and y = mL of pure alcohol

x + y = 560 (total mL is 560)

.6x + y = .65(560) (alcohol plus alcohol equals total alcohol in the mixture)

Multiply 2nd equation by 100 to clear the decimals.

60 x + 100y = 65(560)

Solve the 1st equation for either x or y in order to use substitution method:

y = 560 - x

Substitute for y in 2nd equation:

60 x + 100(560 - x) = 65(560)

60 x - 100x +100(560) = 65(560)

-40x = 65(560) - 100(560)

-40 x = 560(-35)

x = 560(-35)/-40 = 14(35) = 490

So pure alcohol:

y = 560 - 490 = 70

Check:

60% of 490 = 294 mL

plus

70 mL pure alcohol

gives 364 mL of alcohol from the two sources

The final mix:

65% of 560 = 364 mL