Question 244989
x = liters of first solution.
y = liters of second solution.


formula for amount of alcohol required in the new solution is:


.10 * x + .18 *y = .15 * 20


formula for total amount of solution required is:


x + y = 20


you have 2 equations that have to be solved simultaneously.


since x + y = 20, this means that y = 20-x


substitute in the other equation and solve for x.


.10 * x + .18 *y = .15 * 20 becomes:


.10 * x + .18 * (20-x) = .15 * 20


simplify to get:


.10 * x + .18 * 20 - .18 * x = .15 * 20


simplify further to get:


.10 * x + 3.6 - .18 * x = 3


combine like terms to get:


-.08 * x + 3.6 = 3


subtract 3.6 from both sides of the equation to get:


-.08 * x = -.6


divide both sides of this equation by -.08 to get


x = -.6 / -.08 = 7.5


if x = 7.5, then y = 20-7.5 = 12.5


we have x = 7.5 litres and y = 12.5 liters


substitute in original solution equation to get:


.10 * x + .18 *y = .15 * 20 becomes:


.10 * 7.5 + .18 * 12.5 = .15 * 20


simplify to get:


.75 + 2.25 = 3 which is true so the answer is confirmed to be good.


.1 * 7.5 liters of solution 1 + .18 * 12.5 liters of solution 2 = .15 * 20 liters.


you need 7.5 liters of solution 1 and 12.5 liters of solution 2 to make a total of 20 liters.


The percent alcohol will be .1 * 7.5 + .18 * 12.5 = 3 liters of alcohol.


3 liters / 20 liters = 15% of the new solution.