Question

Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.

Answer 1

Let the greater number be x and the smaller number be y. 

By the first condition:

Two numbers differ by 3.

x − y = 3      ...(1)

By the second condition:

The sum of twice the smaller number and thrice the greater number is 19.

2y → Twice the smaller number + 3x → Thrice the greater number = 19

2y + 3x = 19

3x + 2y = 19      ...(2)

Multiplying equation (1) by 2

2x − 2y = 6       ...(3)

Adding equations (2) and (3)

3x + 2y = 19
2x − 2y =  6  
5x         = 25

x = `25/5`

x = `5`

Put x = 5 in equation (1)

x − y = 3

5 − y = 3

y = 5 − 3

y = 2

∴ The greater number is 5, and the smaller number is 2.