1. The sum of two numbers is 60. The greater number is 8 more than thrice the smaller number. Find the numbers.

Solution: Let the two numbers be x and y such that x > y.
Then from the first condition,
x + y = 60 ............. eq. no. (1)
From the second condition,
x = 3y + 8
x – 3y = 8 ............... eq. no. (2)
Subtracting equation (2) from equation (1),
x + y = 60
x – 3y = 8
(-)  (+)   (-)
    4y  = 52
  y = 52/4
y = 13
Substituting y = 13 in equation (1),
x + y = 60
x + 13 = 60
x = 60 – 13
x = 47

The greater number is 47 and the smaller number is 13. 

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