Question

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?




W.
X.

Y.
Z.

Answer 1

To represent the situation of raising at least $500 through corporate and individual sponsorships mathematically, we can define the following variables:

- Let \( x \) be the number of corporate sponsorships.
- Let \( y \) be the number of individual sponsorships.

The total amount raised from corporate sponsorships is \( 100x \) and from individual sponsorships is \( 25y \). The inequality we need to represent is:

\[ 100x + 25y \geq 500 \]

To simplify this inequality, we can divide all terms by 25:

\[ 4x + y \geq 20 \]

### Graphing the Inequality:

1. **Finding the boundary line**: The equation \( 4x + y = 20 \) can be rearranged to find the y-intercept and x-intercept.
- **Y-intercept**: Set \( x = 0 \) → \( y = 20 \) (point (0, 20))
- **X-intercept**: Set \( y = 0 \) → \( 4x = 20 \) → \( x = 5 \) (point (5, 0))

2. **Drawing the line**: Plot the points (0, 20) and (5, 0) on a graph and draw a straight line between them.

3. **Shading the region**: Since we are looking for where \( 4x + y \geq 20 \), we shade the area above the line.

### Conclusion:
The correct graph will have a line that passes through the points (0, 20) and (5, 0), with the region above this line shaded to represent all the combinations of corporate and individual sponsorships that allow raising at least $500.

Please check the provided graphs (W, X, Y, Z) to find which one matches this description. Look for the line passing through (0, 20) and (5, 0), with shading above this line.