Question 766533
you have 2 equations:
x + y = 100
.1x + .6y = 20


x is the number of milliliters of 10% solution.
y is the number of milliliters of 60% solution.


100 milliliters of 20% solution yields 20 milliliters of alcohol.


solve these 2 equations simultaneously to get your answer.
use the elimination method as shown below:


x + y = 100 (equation 1)
.1x + .6y = 20 (equation 2)


multiply equation 2 by 10 to get equation 3 as shown below:
x + 6y = 200 (equation 3)


subtract equation 1 from equation 3 as shown below:


x + 6y = 200 (e3)
x + y = 100 (e4)


result of the subtraction is:
5y = 100 (equation 5)
divide both sides of this equation by 5 to get:
y = 20


substitute for y in equation 1 to get:
x + y = 100 becomes:
x + 20 = 100
solve for x to get:
x = 80


your solution is :
x = 80
y = 20


you need 80 milliliters of 10% solution and 20 liters of 60% solution to get 100 milliliters of 20% solution.


x + y = 80 + 20 = 100 ml of solution
.1x + .6y = .1(80) + .6(20) = 8 + 12 = 20 ml of alcohol