Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake. Diego is waiting in line and is the 23rd customer. He thinks that he should get farther back in line in order to get a prize. Is he right? If so, how far back should he go to get at least one prize? Explain your reasoning.

Diego is correct, he should move back one space.

Step-by-step explanation:

If every 5th customer gets a free bagel then you should be able to count up by 5s to figure out which people get the bagel. (5, 10, 15, etc.)

It would be the same for 9 and 12 (9, 18, 27, etc.) (12, 24, 36, etc.).

However, 23 is not divisible by 5, 9, or 12 (I moved on to division because it's the fast way to check)

But if you look at the multiples of 12 then you'll see that the 24th person would get a prize.

So, Diego should go back one space in order to get a prize because 23 is not  a multiple of 5, 9, or 12. However, 24 is a multiple of 12.

Hope this helps and makes sense.  

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