SOLUTION: The sum of two integers is 120. One half the smaller number plus three-fourths the larger number is 80. What is the smaller number?

Question 202855: The sum of two integers is 120. One half the smaller number plus three-fourths the larger number is 80. What is the smaller number?
Found 2 solutions by rfer, RAY100:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
let x = smaller number
let y = larger number
x+y=120 smae as x=120-y
.5x+.75y=80
-----------------
.5(120-y)+.75y=80
60-.5y+.75y=80
.25y=20
y=80
------------------
x+80=120
x=40
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
1) x+y=120,,,,,x=120-y
2) (1/2)x +(3/4)y=80
.
subst (1) into (2)
.
(120-y)/2 + (3/4)y =80
60-y/2 +(3/4)y =80
y/4 = 20
y=80,,,,,,x=120-80=40
.
check (1) 40 + 80 = 120,,,ok
(2) 40/2 + (3/4) 80 = 20 + 60 = 80,,,,ok

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