SOLUTION: The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.

Question 261261: The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.
.
Let x = first number
and y = second number
.
x+y = 92 (equation 1)
(1/5)x + (1/2)y = 34 (equation 2)
.
Solving equation 1 for y:
x+y = 92
y = 92-x
.
Substitute the above into equation 2 and solve for x:
(1/5)x + (1/2)y = 34
(1/5)x + (1/2)(92-x) = 34
Multiplying both sides by 10:
2x + 5(92-x) = 340
2x + 460 - 5x = 340
460 - 3x = 340
-3x = -120
x = 40
.
Substitute back into equation 1 to find y:
x+y = 92
40+y = 92
y = 52
.
Your two numbers sare 40 and 52
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