Question

Paper plates are sold in packages of 55.

Paper bowls are sold in packages of 50.
Compostable spoons are sold in packages of
100. How many packages of each do you need to buy to have the same number of plates, bowls, and spoons?
(Give your answer as a whole number.)

Number of packages of paper plates:

Number of packages of paper bowls:

Number of packages of compostable spoons:

Answer 1

To have the same number of plates, bowls, and spoons, you would need to buy 20 packages of paper plates, 22 packages of paper bowls, and 11 packages of compostable spoons.

Step-by-step explanation:

To have the same number of plates, bowls, and spoons, we need to find the least common multiple (LCM) of 55, 50, and 100.

The prime factorization of 55 is 5 * 11.

The prime factorization of 50 is 2 * 5^2.

The prime factorization of 100 is 2^2 * 5^2.

From the prime factorizations, we can see that the LCM must include 2^2, 5^2, and 11.

Therefore, the LCM is 2^2 * 5^2 * 11 = 4 * 25 * 11

= 1100.

So, to have the same number of plates, bowls, and spoons, you would need to buy:

• Number of packages of paper plates: 1100 / 55 = 20
• Number of packages of paper bowls: 1100 / 50 = 22
• Number of packages of compostable spoons: 1100 / 100 = 11