Question

1. 14: 14 28·

4: 4 8 12 16 20·24 28 1 cm 28

1. derek shopping for hot dogs and buns. he is surprised to find that the hot dogs come in packs of 8, while the buns come in packs of 12. how many hot dogs and buns will derek have to buy if he wants to have the same number of each?

Explanation:

Step1: Find LCM of 8 and 12

Prime factors: $8=2^3$, $12=2^2\times3$
$\text{LCM}(8,12)=2^3\times3=24$

Step2: Calculate hot dog packs

$\text{Number of packs}=\frac{24}{8}=3$
Total hot dogs: $3\times8=24$

Step3: Calculate bun packs

$\text{Number of packs}=\frac{24}{12}=2$
Total buns: $2\times12=24$

Answer:

Derek needs to buy 24 hot dogs (3 packs) and 24 buns (2 packs) to have the same number of each.