SOLUTION: I am a two-digit number. You can count to me by 4's plus 3 or by 5's plus 3. What is the smallest number I can be? How many different numbers can I be? Explain your answers.

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Question 710743: I am a two-digit number. You can count to me by 4's plus 3 or by 5's plus 3. What is the smallest number I can be? How many different numbers can I be? Explain your answers.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe the problem means that if you count by 4's for a while and then add 3, you get to the number,
and if you count by 5's for a while and then add 3, you also get to the number.
In both cases, before adding 3, you had arrived to a number that was a multiple of 4, and a multiple of 5.
The smallest such number is 4%2A5=20 , and adding 3 to 20 we get
20%2B3=highlight%2823%29
That is the smallest number that you can arrive to by
counting by 4's and adding 3,
and also by counting by 5's and adding 3.
The other larger such numbers are any multiple of 20 plus 3
2%2A20%2B3=40%2A3=highlight%2843%29
3%2A20%2B3=60%2A3=highlight%2863%29 and
4%2A20%2B3=80%2A3=highlight%2883%29
The next such number,
5%2A20%2B3=100%2A3=103 , is not a two-digit number.
So the number in the problem can be any of those 4 numbers:
23 (the smallest), or 43, or 63, or 83.