The question displayed in the image is:

"Suppose that hot dogs come in packs of 10 and buns come in packs of 12. Chris bought the same number of hot dogs as buns. It was the least number of each for which this was possible.

Answer the following questions:

1. How many hot dogs did he buy?
2. How many packs of hot dogs did he buy?
3. How many packs of buns did he buy?"

To solve this, we need the Least Common Multiple (LCM) of 10 and 12, as this gives us the smallest number of hot dogs and buns that are equal and can be divided by their respective pack sizes.

Solution

1. Calculate the LCM of 10 and 12:

   • Prime factorization:
     • $10 = 2 \times 5$
     • $12 = 2^2 \times 3$
   • The LCM is $2^2 \times 3 \times 5 = 60$.

2. Answer each question based on the LCM:

   • How many hot dogs did he buy?
     • He bought 60 hot dogs (since 60 is the smallest quantity that fits in both pack sizes).
   • How many packs of hot dogs did he buy?
     • $60 \div 10 = 6$ packs.
   • How many packs of buns did he buy?
     • $60 \div 12 = 5$ packs.

Answers:

1. He bought 60 hot dogs.
2. He bought 6 packs of hot dogs.
3. He bought 5 packs of buns.

Would you like further clarification on this solution?

Related Questions:

1. What is the LCM of two numbers, and how is it used in similar problems?
2. How do you determine the number of packs needed for a different quantity of hot dogs or buns?
3. What would happen if hot dogs came in packs of 8 instead of 10?
4. If Chris needed to buy a different number of buns than hot dogs, how would the calculation change?
5. How can understanding prime factorization help in solving LCM problems?

Tip: For word problems involving packs or groups, the LCM often helps determine the smallest shared quantity.