SOLUTION: 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???

Question 140813: 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???
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Did you mean that the 'sum of the digits of a two digit number is 10'? I hope so, otherwise what you said makes no sense at all.

x is the tens digit
y is the ones digit

x + y = 10

The number itself is 10x + y

Subtract 18: 10x + y - 18

If the digits are the same after subtracting 18, then x - 1 = y - 8 => x - y = -7 (if y >=8) or x - 2 = y + (10 - 8) => x - y = 4 (if y < 8)

so, if y >= 8
x - y = -7
x + y = 10
2x = 3 => x not an integer, and y must be less than 8

so
x - y = 4
x + y = 10
2x = 14
x = 7
y = 3
The number is 73.

Check
7 + 3 = 10
73 - 18 = 55

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