Question

The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260. Find the numbers.

Answer 1

Let the numbers be x and y.

Then, according to given condition, we have

x + y = 34  ...(i)

and (x – 3)(y + 2) = 260  ...(ii)

On substituting the value of y from equation (i) in equation (ii), we get

(x – 3)(34 – x + 2) = 260  ...[∵ y = 34 – x]

⇒ (x – 3)(36 – x) = 260

⇒ 36x – x² – 108 + 3x = 260

⇒ x² – 39x + 368 = 0

⇒ x² – (16x + 23x ) + 368 = 0

⇒ x² – 16x – 23x + 368 = 0

⇒ x(x – 16) – 23(x – 16) = 0

⇒ (x – 16)(x – 23) = 0

⇒ x = 16 or x = 23

When x = 16, then y = 34 – 16 = 18

When x = 23, then y = 34 – 23 = 11

So, the numbers are 16, 18 or 23, 11.