So, on each occasion, it looks like Smoe had a different number of dog-walking sessions.
Let's try reasoning by using guess-and-check. Do you think each dog-walking session could have cost $1? That means when he made $48, he had 48 sessions. He had a whopping 112 sessions when he made $112. Now, we hope Smoe is smarter than that, so we want to ask ourselves, what's the most he could have charged for a dog-walking session. $5? $10? $20?
Let's start out with our biggest guess. $20. If he charged that much, then on the day he made $80, how many sessions did he have? We'd do $80/$20 to discover he had 4 dog-walking sessions. But $48/$20 and $112/$20 don't divide evenly, and he can't give a fraction of a dog-walking session, so we can conclude that $20 is not the fee for a session.
We can quickly see that our guesses of $5 and $10 aren't correct either because they don't divide evenly into all three dollar amounts. So the number you need for you answer is called "the greatest common factor" of 48, 80, and 112. Hope you can find in your textbook how to find the "GCF," or you can continue to use the guess-and-check method.
Hint: I'll give you an example of how to find the GCF of 60 and 135.
Factor 60 to its smallest components. 60 = 5*12. I can break down 12 into 4*3.
60 = 5*4*3. I can break down 4 into 2*2.
60 = 5*3*2*2. That's as far as I can go. This process is called "prime factorization" because the factors are prime numbers.
135 = 5*27. I can break down 27 into 3*3*3
135 = 5*3*3*3.
Now compare the prime factorizations of 60 and 135.
5*3*2*2 and 5*3*3*3. What factors do they have in common? They have one 5 in common and one 3 in common, 5 and 3. What is the product of their common factors? 5*3=15. Hence, 15 is the GCF of 60 and 135.
