Question

Olivia and her three siblings bring a sack lunch to school each day, consisting of a bagel, an apple, a cookie, and a juice box. When Olivia's mom goes grocery shopping, she likes to purchase the same amount of each lunch item so that she can make complete lunches, with no leftover items. However, each item comes in a different sized package, as shown below:

Bagels: six in a bag
Apples: eight in a bag
Cookies: twelve in a box
Juice Boxes: nine in a box
Find the least number of packages she must purchase in order to have the same amount of each item. Then, complete each statement.

With the amount of items Olivia's mom is purchasing, she'll be able to make enough lunches to feed all four siblings for how many days?

Answer 1

wow OK so the first number I came to was 72 so that's
bagels 6x12=72
apples 8x9=72
cookies 12x6=72
juice boxes 9x8=72

72/4=18 so she could make their lunch for 18 days

Answer 2

Olivia's mom can feed the siblings for 18 days.

Explanation:

We will find the LCM of 6,8,12 and 9.

6 = 2 x 3

8 = 2 x 2 x 2

12 = 2 x 2 x 3

9 = 3 x 3

LCM = 2 x 2 x 2 x 3 x 3 = 72

Now there are 6 bagels in a bag, so Olivia's mom will need =
`72/6=12` bags

Similarly she will need =
`72/8=9` bags of apples.

Cookies boxes needed =
`72/12=6`

Juice boxes needed =
`72/9=8`

She will be purchasing 72 packages in all to feed 4 kids.

Hence, the food will last for
`72/4=18` days.

Olivia's mom can feed the siblings for 18 days.