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.
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Let x = first number
and y = second number
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x+y = 92  (equation 1)
(1/5)x + (1/2)y = 34   (equation 2)
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Solving equation 1 for y:
x+y = 92
y = 92-x
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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  
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Substitute back into equation 1 to find y:
x+y = 92
40+y = 92
y = 52
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Your two numbers sare 40 and 52