Question

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Question 1
Kelly is attending a fall carnival with only $10. Admission into the carnival is $3 and each game inside the carnival costs $0.25.

Which inequality can be used to determine the maximum number games Kelly can play?

(1 point)
Responses

0.25x+3≤10
0 point 2 5 x plus 3 is less than or equal to 10

0.25x+3≥10
0 point 2 5 x plus 3 is greater than or equal to 10

0.25x+3<10
0.25x+3<10

0.25x+3>10
0 point 2 5 x plus 3 is greater than 10
Question 2
(1 point)
Kelly has enough money to play at most
games.
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page 3 of 3

Answer 1

To solve the problem, let's break it down step by step.

1. **Admission cost**: Kelly needs to pay $3 to enter the carnival.
2. **Amount left for games**: After paying for admission, Kelly has $10 - $3 = $7 left.
3. **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 \( 0.25x + 3 \leq 10 \):

1. Subtract 3 from both sides:
\[
0.25x \leq 7
\]

2. 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**.