SOLUTION: The sum of the digits of a four-digit number is 27. If the ten's digit and the unit's digit are reversed, the resulting number exceeds the original number by 45. What is the LARGES
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Question 222733: The sum of the digits of a four-digit number is 27. If the ten's digit and the unit's digit are reversed, the resulting number exceeds the original number by 45. What is the LARGEST possible value for the original four-digit number? Explain your answer. Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! Let t=tens number and u=units number
10t+u=10u+t-45
9t=9u-45
t=u-5 for the last 2 numbers
We want the first 2 numbers to be 99 if possible in order to have the largest number possible.
So t+u=9 would be best.
u-5+u=9 substitute u-5 for t
2u-5=9
2u=14
u=7
t=2
The number is 9927
.
Ed
