Mrs. Morton has a special reward system for her class. When all her students behave well, she rewards them by putting \[3\] marbles into a marble jar. When the jar has \[100\] or more marbles, the students have a party. Right now, the jar has \[24\] marbles.

**Write an inequality to determine the number of additional times, \[r\], Mrs. Morton could reward the class in order for the students to have a party.**

**Will the students have a party if Mrs. Morton rewards them \[31\] additional times?**

Choose 1 answer:

Choose 1 answer:

(Choice A)   

Yes

A

Yes

(Choice B)   

No

B

No

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### Step 1: Write the inequality.

Mrs. Morton adds 3 marbles to the jar each time the students behave well. Currently, there are 24 marbles in the jar. We need to find out how many more times, denoted by \( r \), she can reward the class until the jar has 100 or more marbles.

The total number of marbles after \( r \) additional rewards will be \( 24 + 3r \). For the students to have a party, this amount must be at least 100 marbles. We can write the inequality as:
\[
24 + 3r \geq 100
\]

### Step 2: Solve the inequality.

First, subtract 24 from both sides to isolate the term with \( r \):
\[
3r \geq 100 - 24
\]
\[
3r \geq 76
\]

Next, divide both sides by 3 to solve for \( r \):
\[
r \geq \frac{76}{3}
\]
\[
r \geq 25.33
\]

Since \( r \) represents the number of times she can reward the class, it must be a whole number. Therefore, Mrs. Morton needs to reward the class at least 26 times for the students to have a party.

### Step 3: Determine if the students will have a party after 31 additional rewards.

If Mrs. Morton rewards the class 31 times, substitute \( r = 31 \) into the inequality:
\[
24 + 3(31) = 24 + 93 = 117
\]

Since 117 is greater than 100, the students **will** have a party.

### Final Answer:

**Choice A: Yes**

Would you like more details or have any questions?

Here are five related questions:
1. What if the jar started with 50 marbles—how many rewards would be needed then?
2. If Mrs. Morton only added 2 marbles per reward, how many rewards would be needed for a party?
3. How many marbles would be in the jar after 20 rewards?
4. What if the jar had 150 marbles already—would the students need any more rewards?
5. How many additional rewards would be needed if the party threshold was 200 marbles?

**Tip:** When solving inequalities, remember to check if the solution makes sense in the context, such as needing whole numbers for counting.

Explore how Mrs. Morton rewards her class based on a marble jar system. Solve the inequality to determine how many more times she needs to reward her class for a party. Learn step-by-step with detailed calculations and find out if rewarding the class 31 more times will lead to a party.

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