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.