Solution: Calculating Stationery Pages Needed
This problem requires calculating the rate of stationery usage to determine how long it takes for a different number of students to use a specific amount of stationery.
Step 1: Determine the Rate of Stationery Usage
The relationship between total pages ($S$), number of students ($N$), number of days ($D$), and the rate of usage ($R$) per student per day is:
$S = R \times N \times D$
We are given that $m$ students require $m$ pages in $m$ days.
- $S = m$
- $N = m$
- $D = m$
Substitute these values to find the rate $R$:
$m = R \times m \times m$
$m = R \times m^2$
Solve for $R$:
$R = \frac{m}{m^2} = \frac{1}{m}$ pages per student per day.
Step 2: Calculate Required Days for 100 Students
We need to find the number of days ($D$) for 100 students to use 100 pages, using the rate $R = \frac{1}{m}$.
- $S = 100$
- $N = 100$
- $R = \frac{1}{m}$
- $D = ?$
Using the formula $S = R \times N \times D$:
$100 = \frac{1}{m} \times 100 \times D$
$100 = \frac{100}{m} \times D$
Step 3: Solve for the Number of Days (D)
Rearrange the equation to solve for $D$:
Multiply both sides by $m$:
$100 \times m = 100 \times D$
Divide both sides by 100:
$D = \frac{100 \times m}{100}$
$D = m$
Final Answer
100 students will require 100 pages of stationery in $m$ days. This matches Option 4.
