SOLUTION: Please help me with this problem. I've tried working on it but all I end up with is a headache. The sum of the digits of a two-digit number is 8. If 16 is added to the original nu

Question 151854: Please help me with this problem. I've tried working on it but all I end up with is a headache.
The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number.
;
Let x = 10's digit
Let y = units digit
;
two digit number = 10x + y
:
Sum of digits:
x + y = 8
or
y = (8-x)
:
Write an equation for the statement:
"If 16 is added to the original number, the result is 3 times the original number with its digits reversed."
10x + y + 16 = 3(10y + x)
:
10x + y + 16 = 30y + 3x
:
10x - 3x + 16 = 30y - y
:
7x = 29y - 16
:
Find the original number.
:
substitute (8-x) for y in the above equation
7x = 29(8-x) - 16
:
7x = 232 - 29x - 16
:
7x + 29x = 232 - 16
:
36x = 216
x =
x = 6, then, of course, y = 2
:
Original number = 62
;
:
Check solution in the statement:
If 16 is added to the original number, the result is 3 times the original number with its digits reversed."
62 + 16 = 3(26)
78 = 78
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