SOLUTION: Two fractions have the same the denominator, 8. The sum of the two fractions is ½. If one of the fractions is added to five times the other, the result is 2. Find the two fraction

Algebra ->  Test -> SOLUTION: Two fractions have the same the denominator, 8. The sum of the two fractions is ½. If one of the fractions is added to five times the other, the result is 2. Find the two fraction      Log On


   

Question 1151932: Two fractions have the same the denominator, 8. The sum of the two fractions is ½. If one of the fractions is added to five times the other, the result is 2. Find the two fractions.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x/8 represent the first fraction and let y/8 represent the second fraction.

you have 2 equations that need to be solved simultaneously.

they are:

x/8 + y/8 = 1/2
x/8 + 5y/8 = 2

subtract the first equation from the second to get:
4y/8 = 3/2
multiply both sides of this equation by 8 to get:
4y = 8 * 3/2
simplify to get:
4y = 24/2
simplify further to get:
4y = 12
solve for y to get y = 3
replace y with 3 in the first equation to get:
x/8 + 3/8 = 1/2
solve for x to get:
x = 1
replace x with 1 and y with 3 in the second equation to get:
1/8 + 5 * 3/8 = 2
simplify to get:
1/8 + 15/8 = 2
combine like terms to get:
16/8 = 2
both equations are true when x = 1 and y = 3.
your solution is that the two fractions are 1/8 and 3/8.