Bryan is buying notebooks and pens at an office supply store. Notebooks cost $3.59 and pens cost $1.49. He can spend up to $13 on these items.

Question

Let x represent the number of notebooks. Let y represent the number of pens.

Answer 1

To represent the problem mathematically, we can set up an inequality based on Bryan's spending limit.

The cost of notebooks is $3.59 each, so the total cost for \( x \) notebooks is \( 3.59x \). The cost of pens is $1.49 each, so the total cost for \( y \) pens is \( 1.49y \).

Bryan can spend up to $13, which gives us the following inequality:

\[ 3.59x + 1.49y \leq 13 \]

Interpretation of Variables

• \( x \): Number of notebooks Bryan buys
• \( y \): Number of pens Bryan buys

Constraints

If we consider the context, \( x \) and \( y \) should also be non-negative integers (since you can't buy a negative number of notebooks or pens):

\[ x \geq 0 \quad \text{and} \quad y \geq 0 \]

Summary

The final representation of the situation is:

1. The inequality representing the spending limit: \[ 3.59x + 1.49y \leq 13 \]

2. The constraints for non-negative integers: \[ x \geq 0 \quad \text{and} \quad y \geq 0 \]

This model can be used to explore different combinations of notebooks and pens that Bryan can purchase without exceeding his budget.