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:


We need to find the number of additional times Mrs. Morton can reward her class so that the total number of marbles in the jar reaches or exceeds 100.

### Step 1: Define Variables
- Let \( r \) be the number of additional rewards Mrs. Morton will give.
- Each reward adds 3 marbles to the jar.

### Step 2: Write the Inequality
Initially, there are 24 marbles in the jar. Each reward adds 3 marbles, so after \( r \) additional rewards, the total number of marbles in the jar will be:
\[
24 + 3r
\]
To have a party, the number of marbles must be at least 100. Therefore, we need:
\[
24 + 3r \geq 100
\]

### Step 3: Solve the Inequality
To solve for \( r \):
\[
24 + 3r \geq 100
\]
First, subtract 24 from both sides:
\[
3r \geq 76
\]
Now, divide both sides by 3:
\[
r \geq \frac{76}{3} \approx 25.33
\]
Since \( r \) must be a whole number, we round up to the next integer. So, Mrs. Morton must reward the class at least **26** additional times for the students to have a party.

### Step 4: Check for \( r = 31 \)
Now, let's check if the students will have a party after 31 additional rewards. Substituting \( r = 31 \) into the expression for the total number of marbles:
\[
24 + 3(31) = 24 + 93 = 117
\]
Since 117 is greater than 100, **yes**, the students will have a party if Mrs. Morton rewards them 31 additional times.

### Conclusion:
- The inequality is \( 3r + 24 \geq 100 \).
- Yes, the students will have a party if Mrs. Morton rewards them 31 additional times.

---

Do you want more details on any part of the process?

Here are some related questions for practice:
1. What if each reward added 5 marbles instead of 3?
2. How many total marbles will be in the jar after 40 rewards?
3. What is the smallest number of additional rewards needed if the jar initially had 50 marbles?
4. How would the inequality change if the party threshold was 150 marbles?
5. What if Mrs. Morton removed 2 marbles for every bad behavior?

**Tip:** Always check if the final result makes sense by plugging the solution back into the original context!

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?

Solve an algebraic inequality problem where Mrs. Morton rewards her class with 3 marbles for good behavior. Find how many more rewards are needed to reach 100 marbles and whether the class can have a party with 31 additional rewards. Suitable for students in Grades 6-8, this problem covers linear equations and inequalities.

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