Question

Sum of a two digit number is 10. If 18 is subtracted from the number then the digits of the new number become equal. Find the original number.

Answer 1

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Let x = 10's digit of a two digit number

Let y = units digit

Let z = the resulting equal digits

:

Write an equation for each statement:

:

"the sum of a two digit number is 10."

x + y = 10

or

y = (10-x)

:

" if 18 be subtracted from it, the digits in the resulting number will be equal."

10x + y - 18 = 10z + z

10x + y = 11z + 18

:

Substitute (10-x) for y

10x + (10-x) = 11z + 18

10x - x = 11z + 18 - 10

9x = 11z + 8

:

The single digit integer values for x and z are limited to x=7 and z=5 in this equation:

x = 7, y = 3, z = 5

:

The number is 73

:

Check in the statement:

"if 18 be subtracted from it, the digits in the resulting number will be equal."

73 - 18 = 55