https://file.aiquickdraw.com/mathbot/file/17290012270978xlnz8ci.jpg

Let's analyze the given problem:

**Problem Summary:**
- Emma bought 3 packages of balloons ($ b $) and 4 tablecloths ($ t $) for $14.63.
- Nathan bought 2 packages of balloons and 5 tablecloths for $16.03.

**We need to find a system of equations that represents these purchases to solve for the price of each package of balloons ($ b $) and each tablecloth ($ t $).**

**Writing the equations:**
1. Emma's purchase: $ 3b + 4t = 14.63 $
2. Nathan's purchase: $ 2b + 5t = 16.03 $

The correct system of equations should have the above format. Comparing this to the given choices:

- The correct choice is:
  \[
  3b + 4t = 14.63 \quad \text{and} \quad 2b + 5t = 16.03
  \]

This matches the second option provided in the problem.

Would you like a detailed solution on how to solve this system of equations?

Here are 5 related questions to consider:
1. How do you solve a system of equations using substitution?
2. What is the elimination method for solving systems of equations?
3. How can you verify if a solution is correct for a system of equations?
4. What are the graphical methods for solving systems of linear equations?
5. How do different values in a system of equations affect the solution?

**Tip:** When solving a system of equations, always double-check your equations match the problem description accurately.

Emma and Nathan went to a party supply store to buy decorations for the spring dance. Emma bought 3 packages of balloons (b) and 4 tablecloths (t) for $14.63. Nathan bought 2 packages of balloons and 5 tablecloths for $16.03. Which choice could be used to solve for the price of each package of balloons and each tablecloth?

Learn how to solve a system of equations based on Emma and Nathan's purchases of balloons and tablecloths for a spring dance. Use algebraic methods to determine the price of each item. Suitable for students in Grades 7-9.

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