SOLUTION: James needs to mix a 10% alcohol solution with a 60% alcohol solution to create 100 millileters of a 20% solution. How many millileters of each solution must James use? A) Write

Question 766533: James needs to mix a 10% alcohol solution with a 60% alcohol solution to create 100 millileters of a 20% solution. How many millileters of each solution must James use?
A) Write an equation using the information as it is given above that can be used to solve this problem. Use as your variable to represent the quantity of 10% alcohol solution.
Equation:

B) Answer: James must mix HOW MANY millileters of 10% solution and HOW MANY millileters of 60% solution?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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