SOLUTION: The sum of the digits of a two-digit counting number was 9. When the digits were reversed, the new number was 45 less than the original number. What was the original number?

Question 68268This question is from textbook An Incremental Development
: The sum of the digits of a two-digit counting number was 9. When the digits were reversed, the new number was 45 less than the original number. What was the original number? This question is from textbook An Incremental Development

Found 2 solutions by Nate, ankor@dixie-net.com:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Two Digit Number: 10a + b
a + b = 9 or a = 9 - b
10b + a = 10a + b - 45
Plug:
10b + 9 - b = 10(9 - b) + b - 45
9b + 9 = 90 - 10b + b - 45
9b + 9 = 45 - 9b
18b = 36
b = 2
a = 7
Number: 72
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

Let x = the 1st digit; y = 2nd digit
:
"The sum of the digits of a two-digit counting number was 9."
x + y = 9
x = (9 - y)
:
original number: 10x + y
Reversed number: 10y + x
:
"the digits were reversed, the new number was 45 less than the original number"
(10y + x) + 45 = 10x + y
:
Perform operations to get variables on the left and number on the right
10y - y + x - 10x = -45
9y - 9x = -45
:
Simplify divide equation by 9:
y - x = -5
:
Substitute (9-y) for x:
y - (9-y) = -5
y - 9 + y = -5
2y = -5 + 9
2y = +4
y = 2
:
Find x: 9 - 2 = 7
:
Original number 72, reversed number 27
:
Check: 72 - 27 = 45

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