Question

Find two numbers such that if 18 is added to the first number it becomes twice the second number and if 16 is added to the second number it becomes three times the first number.

Answer 1

10 and 14

Explanation:

Let the first number be x and the second number be y, then

x + 18 = 2y → (1)

y + 16 = 3x → (2)

Rearrange (1) expressing x in terms of y by subtracting 18 from both sides

x = 2y - 18 → (3)

Substitute x = 2y - 18 into (2)

y + 16 = 3(2y - 18) ← distribute

y + 16 = 6y - 54 ( subtract 6y from both sides )

- 5y + 16 = - 54 ( subtract 16 from both sides )

- 5y = - 70 ( divide both sides by - 5 )

y = 14

Substitute y = 14 into (3) for corresponding value of x

x = (2 × 14) - 18 = 28 - 18 = 10

The 2 numbers are 10 and 14