To solve this, we need to set up inequalities based on the information given:
1. The total amount donated to both charities is up to $480, so:
\[ x + y \leq 480 \]
2. The amount donated to the Educational Growth Foundation should be at least three times the amount donated to the City Youth Fund:
\[ y \geq 3x \]
Now, let's graph these inequalities:
- For \( x + y \leq 480 \), you would draw a line where \( y = 480 - x \) and shade below this line since \( y \) must be less than or equal to \( 480 - x \).
- For \( y \geq 3x \), draw a line where \( y = 3x \) and shade above this line since \( y \) must be at least three times \( x \).
The region where these shaded areas overlap represents the set of all values of \( x \) and \( y \) that satisfy both conditions. This is the feasible region for the donations Karen can make according to her preferences.
