The sum of two numbers is 60. The smaller number is 6 less than the larger number. What are the numbers?

a + b = 60 (1)

b < a with 6 ⇒ b = a - 6 (2)

(1), (2) ⇒ a + a - 6 = 60 ⇒ a + a = 60 + 6 ⇒ 2a = 66 ⇒ a + 66:2 ⇒

⇒ a = 33 (3)

(2), (3) ⇒ b = 33 - 6 ⇒ b = 27

So, the numbers are : a = 33, b = 27