Question

The sum of the digits of a two digit number is 10. If 18 be subtracted from the sum of the digits of a two-digit number is 2018 be subtracted from the from which the digits in the resulting number will be equal the number is ​

Answer 1

Answer:

55

Step-by-step explanation:

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

Let y = units digit

Let z = the resulting equal digits

The sum of a two digit number is 10, thus -

x + y = 10  or  y = (10-x)

If 18 be subtracted from it, the digits in the resulting number will be equal. thus -

= 10x + y - 18 = 10z + z

=  10x + y = 11z + 18

Substituting (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

Thus, the number is 73

Checking in the statement: - if 18 be subtracted from it, the digits in the resulting number will be equal = 73 - 18 = 55.

Thus, the resulting number will be 55.