SOLUTION: 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 num
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: 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.
This question is from textbook
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement:
:
Let the original number = 10x + y
:
The sum of the digits of a two-digit number is 8.
x + y = 8
or
x = (8-y); use for substitution
:
"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 = 30y - y - 16
7x = 29y - 16
:
Find the original number.
:
Substitute (8-y) for x in the above equation:
7(8-y) = 29y - 16
56 - 7y = 29y - 16
56 + 16 = 29y + 7y
72 = 36y
y =
y = 2 is the units digit
:
Find x:
8 - 2 = 6 is the 10's digit
:
Our original number is 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; confirms our solution
:
How about this. Did it make it understandable? Could you do a similar problem now?
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