Question

If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?

(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

Answer 1

Number of students will be 12

Step-by-step explanation:

We have given total number of cupcakes = 72

Let total number of students = N

(A) Then cupcakes received by each individual
`=(72)/(N)`

Now according to question number of students are reduced by
`(1)/(3)`, then cupcakes received by each individual students is reduced by 3

So new number of students
`=N-(N)/(3)=(2N)/(3)`

Now according to question
`(72)/((2N)/(3))=N-3`

`=216=2N^2-6N`

`2N^2-6N-216=0`

N = 12 and N = -9

As students can not be negative so N = 12

(B) Now according to second question

`72* 2=12N`

N = 12 students