The sum of the digits of a two-digit number is 16. If the digits are reversed, the new number is 18 less than the original number. Find the original number.

Question

Ninth grade Algebra

Answer 1

Assume, the unit place digit will be y & the ten's place digit will be x

∴  The number will be 10x+y [Think it as, if the number is 13, then 10*1+3 = 13]

& the sum of the digits of the number will be x+y which is equal to 16 (already given)

x+y = 16  ----------- 1)

If the digits are reversed, the new number will be 10y+x

According to the question or the data given,

(10x+y) - (10y+x) = 18

10x + y - 10y -x = 18

Or, 9x - 9y = 18

Or, 9(x - y) = 18

Or, x - y = 18/9 = 2 

Or, x - y = 2 ----------- 2)

Now, add 1) + 2)

x + y + x - y = 16 +2

Or, 2x = 18

Or, x = 9

Putting the value of x = 9 in equation 1)

x + y = 16

Or, 9 + y = 16

Or, y = 16 - 9 = 7

∴ The original number will be 97 & the reversed number is 79