Samantha is raising money for a local charity. She is required to raise at least $500.00 through corporate and individual sponsorships. Each corporate sponsorship raises $100.00, and each individual sponsorship raises $25.00.

Which of the following graphs represents the situation?

1 answer

To represent Samantha's fundraising situation graphically, we need to formulate the relationship based on the information provided regarding corporate and individual sponsorships.

Let's define:

  • \( c \): the number of corporate sponsorships.
  • \( i \): the number of individual sponsorships.

Each corporate sponsorship raises $100.00, so the total amount raised from corporate sponsorships can be expressed as \( 100c \).

Each individual sponsorship raises $25.00, thus the total amount from individual sponsorships is \( 25i \).

Samantha needs to raise at least $500, so we can set up the following inequality:

\[ 100c + 25i \geq 500 \]

We can simplify this inequality by dividing all terms by 25:

\[ 4c + i \geq 20 \]

This inequality represents a half-plane in a coordinate system where \( c \) (corporate sponsorships) is on the x-axis and \( i \) (individual sponsorships) is on the y-axis.

Steps to graph the inequality:

  1. First, identify the equality line \( 4c + i = 20 \):

    • When \( c = 0 \): \( 4(0) + i = 20 \) → \( i = 20 \) (point (0, 20))
    • When \( i = 0 \): \( 4c + 0 = 20 \) → \( c = 5 \) (point (5, 0))
  2. Plot the line connecting points \( (0, 20) \) and \( (5, 0) \).

  3. Since the inequality is \( \geq \), you will shade above this line to represent all combinations of corporate and individual sponsorships that satisfy the requirement of raising at least $500.

  4. Identify that \( c \) and \( i \) must be non-negative integers, so you'll be working in the first quadrant where both \( c \) and \( i \) are 0 or greater.

Resulting Graph:

The graph you are looking for would contain:

  • A line from (0, 20) to (5, 0) representing the boundary \( 4c + i = 20 \).
  • Shading above this line (towards the top right) showing the feasible solutions where the total amount raised is at least $500.
  • The axes indicating only non-negative values for \( c \) and \( i \).

If you provide any options of graphs, I can help you identify which one corresponds to this description.