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Question 444638: The sum of the digits of a two digit number is 15. If the digits are interchanged, the number is increased by nine. What is the original number?
Found 2 solutions by chriswen, oberobic:
Answer by chriswen(106)   (Show Source):
You can put this solution on YOUR website! Let x be the first digit.
Let 15-x be the second digit.
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10x+(15-x)+9=10(15-x)+x ... the 10's column is worth per digit (10 times).
9x+24=150-10x+x
9x+24=150-9x
9x+9x=150-24
18x=126
x=7
15-x=8
...
Therefore, the number is 78.
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! These are fun problems because they force you to reconsider what numbers mean.
Consider 15. What does it mean?
Well, the 1 means 1*10.
And the 5 means 5*1.
So 15 means 1*10 + 5*1 = 10 + 5 = 15.
We can extend this notion to any sequence of letters, for example 'xy'.
.
Do NOT get confused with 'xy' meaning x * y.
Here it would mean 10*x + 1*y.
.
xy = the two-digit number, which
x + y = 15
yx = xy + 9
.
Looking back we realize that x and y have to be single digits. And for them to = 15, they're either
9 + 6
8 + 7
7 + 8
6 + 9
.
When the numbers are reversed, the difference is 9.
.
Take 78, when turned around it is 87, which is 9 more.
.
So xy = 78, which is the original number.
The sum 7+8 = 15.
When the order is reversed (i.e., 87) the value is 9 more than before the reversal.
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