To determine the amount of marbles each person receives when Brett divides [tex]$p$[/tex] coloured marbles equally between [tex]$q$[/tex] people, we need to understand how to distribute a quantity equally among a certain number of recipients.
Here is a step-by-step explanation:
1. Understanding Division in This Context: When you want to divide a total number of items equally among a number of people, you need to use division. Specifically, you divide the total number of items (marbles, in this case) by the number of people.
2. Mathematical Representation: Let [tex]\( p \)[/tex] represent the total number of marbles, and [tex]\( q \)[/tex] represent the total number of people. To find the amount of marbles each person receives, you divide [tex]\( p \)[/tex] marbles by [tex]\( q \)[/tex] people.
3. Setting Up the Equation: The amount each person receives is given by the formula:
[tex]\[
\text{Amount per person} = \frac{p}{q}
\][/tex]
4. Identifying the Correct Answer:
- Option A: [tex]\(\frac{q}{p}\)[/tex] - This represents the inverse of what we need. It shows how many parts each marble would be divided into if each person got equal parts, which is incorrect.
- Option B: [tex]\(pq\)[/tex] - This represents multiplication, suggesting more marbles than available, which is incorrect.
- Option C: [tex]\(\frac{p}{q}\)[/tex] - This correctly represents the division of the total number of marbles by the total number of people, showing each person's share.
- Option D: [tex]\(p+q\)[/tex] - This adds the two numbers together, not applicable for division of items.
- Option E: [tex]\(p-q\)[/tex] - This subtracts the number of people from the number of marbles, which is not relevant in this context.
Therefore, the correct answer is:
[tex]\[
C \, \frac{p}{q}
\][/tex]
Each person would receive [tex]\(\frac{p}{q}\)[/tex] marbles. Thus, if Brett buys [tex]\( p \)[/tex] coloured marbles and divides them equally among [tex]\( q \)[/tex] people, each person receives [tex]\(\frac{p}{q}\)[/tex] marbles.
