The amount of candy shared by the class varies inversely with the number of students in the class. If there are 120 pieces of candy, how much would each student receive in a class of 30?

Nov 2, 2017

Each student will receive 4 pieces of candy.

Explanation:

Divide the number of pieces (pc) of candy by the number of students.

$\text{120 pc candy"/"30 students"="4 pc candy"/"1 student}$

Nov 2, 2017

Each student receives $4 p c s$ of candy.

Explanation:

The amount of candy $C$ varies inversely with the number $N$ of students in the class.

That tells is immediately that $\frac{C}{N} = 1$.

In this case we are sharing the candy amongst students, so the multiplier is the number of pieces of candy each student receives $R$.

Then our operating equation is $\frac{C}{N} = 1 R = R$

Inserting given values: $\frac{C}{N} = R \to \frac{120 p c s}{30} = R = \left(4 p c s\right)$

So each student receives $4 p c s$ of candy.

If there were only 20 students in the next class sharing the same candy, the same formula could be used:

$\frac{C}{N} = R \to \frac{120 p c s}{20} = R = \left(6 p c s\right)$

So here, each student receives $6 p c s$ of candy.