Question

Torrance is shopping for a school party. His donation to the party is snack bags and juice boxes. Snack bags come in packages of 12, and juice boxes come in a package of 10. What is the fewest number of packages of each product Torrance must purchase so that he has the same number of snack bags and juice boxes? Use paper to show what you know about the least common multiple to support your answer. Enter your answers in the boxes. Torrance must purchase packages of snack bags and packages of juice boxes to have the same number of each

Answer 1

Torrance must purchase 5 packages of snack bags and 6 packages of juice boxes.

Explanation:

Given that:

Snack bags come in packages of 12.

Juice bags come in packages of 10.

To find:

Fewest number of packages of each product so that there are same number of snack bags and juice boxes.

Solution:

Number of snack bags when 1 package is bought = 12

Number of snack bags when 2 package is bought = 24

Number of snack bags when 3 package is bought = 36

Number of snack bags when 4 package is bought = 48

Number of snack bags when 5 package is bought = 60

Number of snack bags when 6 package is bought = 72

Number of juice bags when 1 package is bought = 10

Number of juice bags when 2 package is bought = 20

Number of juice bags when 3 package is bought = 30

Number of juice bags when 4 package is bought = 40

Number of juice bags when 5 package is bought = 50

Number of juice bags when 6 package is bought = 60

Number of juice bags when 7 package is bought = 70

We can see that when 5 packages of snack bags are bought and 6 packages of juice bags are bought, 60 bags of each are bought.

This can be found by finding the LCM as well.

LCM of 10 and 12 is 60.

It means we need to buy 60 bags of each item.

And we can easily find the number of packages for each.

Number of packages of snack bags to be bought =
`(60)/(12) =5`

Number of packages of juice bags to be bought =
`(60)/(10) = 6`

Torrance must purchase 5 packages of snack bags and 6 packages of juice boxes.