Sure! Let's solve this step-by-step:
1. Identify the package sizes:
- Hot dogs are sold in packages of 10.
- Buns are sold in packages of 12.
2. Find the least common multiple (LCM) of the package sizes:
- To have the same number of hot dogs and buns, we want the smallest number of hot dogs that is also a multiple of 12 (the number of buns per package).
- The least common multiple (LCM) of 10 (hot dogs per package) and 12 (buns per package) is 60. This is because 60 is the smallest number that both 10 and 12 divide evenly into.
3. Calculate the number of packages needed for both hot dogs and buns:
- Hot dogs: Since each package has 10 hot dogs, and we need 60 hot dogs,
[tex]\[
\text{Number of hot dog packages} = \frac{60}{10} = 6.
\][/tex]
- Buns: Since each package has 12 buns, and we need 60 buns,
[tex]\[
\text{Number of bun packages} = \frac{60}{12} = 5.
\][/tex]
4. Conclusion:
- To have the same number of hot dogs as buns, you need to buy 6 packages of hot dogs and 5 packages of buns.
Therefore, the smallest number of packages of hot dogs you need to buy if you want to buy the same number of hot dogs as buns is 6 packages.
