The fifth graders at Jefferson School are planning a party. One-half of the students will drink juice at the party. One-fourth of the students will drink milk at the party.

One-eighth of the students will drink lemonade at the party. Twelve of the fifth graders will drink punch at the party. How many students will be having a drink at the party? How many students will drink each kind of drink at the party?

In order to enable us to calculate the total number of students that will be having a drink each at the party, we need to denote the total number of students that will be at the party by "y".

Since 1/2, 1/4, and 1/8 of the total students will be drinking juice, milk and lemonade respectively, then the number of students that will take only juice is:

1/2 × y = y/2

The number of students that will take only milk at the party is:

1/4 × y = y/4

The number of students that will be drinking only lemonade at the party is:

1/8 × y = y/8

We already have the knowledge of the actual number of students that will be drinking punch at the party (which is 12).

Since the total number of students that will be drinking at the party = y, then:

y/2 + y/4 + y/8 + 12 = y

[(4y + 2y + y)/8] + 12 = y

7y/8 + 12 = y

(7y + 96)/8 = y/1

7y + 96 = 8y

8y - 7y = 96

y = 96

Therefore, there will be a total of 96 students that will be having a drink at the party.

Since 1/2 of them will be drinking juice at the party, then the actual number of the students that will take juice is:

1/2 × 96

= 48 (will take juice)

The fraction of students that will take milk is 1/4 therefore the actual number of them that will prefer milk is:

1/4 × 96

= 24 (will take milk)

Since 1/8 of the total students at the party will opt for lemonade, then the actual number that will have lemonade drink is:

1/8 × 9 = 12 (will take lemonade)

The remaining students (12 of them) will be taking lunch.

Let's check: 48 + 24 + 12 + 12 = 96 students