Question

Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers

Answer 1

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

According to the first condition, difference between two numbers is 3.

∴ x – y = 3   .....(i)

According to the second condition, the sum of three times the bigger number and two times the smaller number is 19.

∴ 3x + 2y = 19    .....(ii)

Multiplying equation (i) by 2, we get

2x – 2y = 6   .....(iii)

Adding equations (ii) and (iii), we get

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

∴ x = `25/5`

∴ x = 5

Substituting x = 5 in equation (i), we get

x – y = 3

∴ 5 – y = 3

∴ 5 – 3 = y

∴ y = 2

∴ The required numbers are 5 and 2.