Formulate the following problems as a pair of equations, and hence find their solutions:
One number is greater than thrice the other number by 2. If 4 times the smaller number exceeds the greater by 5, find the numbers.

Question

Formulate the following problems as a pair of equations, and hence find their solutions:
A two digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.

Philoid · Accepted Answer

Let x denote the digit in the tenth place and y denote the digit in the unit place. So the number may be written as 10x + y.

When digits are reversed, the number becomes 10y + x.

First condition is

10x + y = 7 (x + y)

⇒ 10x + y – 7x – 7y = 0

⇒ 3x – 6y = 0

⇒ x – 2y = 0

Second condition is

10y + x = (10x + y) – 18

⇒ 10y + x – 10x – y + 18 = 0

⇒ – 9x + 9y + 18 = 0

⇒ – x + y + 2 = 0

For cross multiplication method, we write the coefficients as

Hence, we get = =

⇒ = =

⇒ x = = 4

⇒ y = = 2

∴ The number is 10x + y = 10 (4) + 2 = 40 + 2 = 42.