Question

Maximum Load on a Stage In $2014$, a high school stage collapsed in Fullerton, California, when $250$students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of $12,750$pounds. If the average weight of a student is assumed to be $140$pounds, what is the maximum number of students who could safely be on the stage?

Short answer

The maximum number of student is $91$.

Step-by-step solution

Step 1. Given Information 

We are given that the maximum weight supported by stage is $12,750$pounds and the average weight of a student is $140$pounds.

We have to find the maximum number of students who could stand safely on the stage.

Step 2. Forming the inequality 

The maximum weight supported by stage is $12,750$,

Let the number of students be x,

The total weight on the stage must be less than or equal to $12,750$.

So, the inequality will be,

$140x\le 12750$

Step 3. Solving the Inequality  

Dividing by $140$, we get

$$\begin{gathered} 140x\le 12750 \\ x\le \frac{12750}{140} \\ x\le 91.02 \end{gathered}$$

The number of students must be a whole number, so

$x=91$

Hence, the maximum number of student who could safely be on the stage is $91$.