To solve the problem, let's break it down step by step.
- Admission cost: Kelly needs to pay $3 to enter the carnival.
- Amount left for games: After paying for admission, Kelly has $10 - $3 = $7 left.
- Cost per game: Each game costs $0.25.
Let \( x \) be the number of games Kelly can play. The total cost for \( x \) games would be \( 0.25x \). To find the maximum number of games she can play, we set up the following inequality:
\[ 3 + 0.25x \leq 10 \]
This simplifies to:
\[ 0.25x \leq 7 \]
Now we can determine which of the provided inequalities is correct:
- Option 1: \( 0.25x + 3 \leq 10 \) is the correct inequality because it represents the total money spent being less than or equal to her total amount ($10).
- Option 2: \( 0.25x + 3 \geq 10 \) is incorrect.
- Option 3: \( 0.25x + 3 < 10 \) is also technically correct but does not represent the maximum number of games because it would allow for games only below the maximum.
- Option 4: \( 0.25x + 3 > 10 \) is incorrect.
Thus, the correct inequality is:
0.25x + 3 ≤ 10
Next, let's compute the maximum number of games Kelly can play:
From the inequality \( 0.25x + 3 \leq 10 \):
-
Subtract 3 from both sides: \[ 0.25x \leq 7 \]
-
Divide both sides by 0.25: \[ x \leq \frac{7}{0.25} = 28 \]
So, Kelly can play at most 28 games.
To summarize:
- Kelly can play at most 28 games.