Question

the sum of a two digit number is 10. if 18 be subtracted from it, the digits in the resulting number will be equal. the number is?

Answer 1

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