Question
Two high schools, A and B, are each trying to raise at least $3,000 for new computers. School A received a $500 donation from the Parents’ Club and will sell stuffed bears at $10 each to raise the remaining money. School B received a $1,250 donation from the Parents’ Club and will sell stuffed monkeys for $7.50 each to raise the remaining money.
• Write an inequality for each school that represents the number of stuffed animals the school must sell to meet or exceed their goal. Solve each inequality, showing all work necessary to justify your answers.
• Compare the minimum number of stuffed animals School A must sell with the minimum number that School B must sell and state which school must sell more stuffed animals. Show all work necessary to justify your answer. Give your solution using a complete sentence
• Write an inequality for each school that represents the number of stuffed animals the school must sell to meet or exceed their goal. Solve each inequality, showing all work necessary to justify your answers.
• Compare the minimum number of stuffed animals School A must sell with the minimum number that School B must sell and state which school must sell more stuffed animals. Show all work necessary to justify your answer. Give your solution using a complete sentence
Answers
GPT-4o mini
To determine how many stuffed animals each school needs to sell to reach their goal of at least $3,000 for new computers, we can set up and solve inequalities for each school.
### School A:
1. **Initial Information:**
- Donation received: $500
- Selling price of stuffed bears: $10 each
- Goal amount: $3,000
2. **Calculate the amount of money still needed:**
\[
\text{Amount needed} = 3000 - 500 = 2500
\]
3. **Inequality:**
Let \( x \) represent the number of stuffed bears sold. The inequality can be expressed as:
\[
10x \geq 2500
\]
4. **Solving the Inequality:**
\[
x \geq \frac{2500}{10}
\]
\[
x \geq 250
\]
Thus, School A must sell **at least 250 stuffed bears.**
### School B:
1. **Initial Information:**
- Donation received: $1,250
- Selling price of stuffed monkeys: $7.50 each
- Goal amount: $3,000
2. **Calculate the amount of money still needed:**
\[
\text{Amount needed} = 3000 - 1250 = 1750
\]
3. **Inequality:**
Let \( y \) represent the number of stuffed monkeys sold. The inequality can be expressed as:
\[
7.5y \geq 1750
\]
4. **Solving the Inequality:**
\[
y \geq \frac{1750}{7.5}
\]
\[
y \geq 233.33
\]
Since the number of stuffed animals sold must be a whole number, we round up:
\[
y \geq 234
\]
Thus, School B must sell **at least 234 stuffed monkeys.**
### Comparison:
- School A must sell at least **250 stuffed bears** while School B must sell at least **234 stuffed monkeys**.
### Conclusion:
Comparing the two values, we find that:
\[
250 > 234
\]
Therefore, **School A must sell more stuffed animals than School B.** Specifically, School A must sell at least 16 more stuffed animals than School B to reach their fundraising goal.
### School A:
1. **Initial Information:**
- Donation received: $500
- Selling price of stuffed bears: $10 each
- Goal amount: $3,000
2. **Calculate the amount of money still needed:**
\[
\text{Amount needed} = 3000 - 500 = 2500
\]
3. **Inequality:**
Let \( x \) represent the number of stuffed bears sold. The inequality can be expressed as:
\[
10x \geq 2500
\]
4. **Solving the Inequality:**
\[
x \geq \frac{2500}{10}
\]
\[
x \geq 250
\]
Thus, School A must sell **at least 250 stuffed bears.**
### School B:
1. **Initial Information:**
- Donation received: $1,250
- Selling price of stuffed monkeys: $7.50 each
- Goal amount: $3,000
2. **Calculate the amount of money still needed:**
\[
\text{Amount needed} = 3000 - 1250 = 1750
\]
3. **Inequality:**
Let \( y \) represent the number of stuffed monkeys sold. The inequality can be expressed as:
\[
7.5y \geq 1750
\]
4. **Solving the Inequality:**
\[
y \geq \frac{1750}{7.5}
\]
\[
y \geq 233.33
\]
Since the number of stuffed animals sold must be a whole number, we round up:
\[
y \geq 234
\]
Thus, School B must sell **at least 234 stuffed monkeys.**
### Comparison:
- School A must sell at least **250 stuffed bears** while School B must sell at least **234 stuffed monkeys**.
### Conclusion:
Comparing the two values, we find that:
\[
250 > 234
\]
Therefore, **School A must sell more stuffed animals than School B.** Specifically, School A must sell at least 16 more stuffed animals than School B to reach their fundraising goal.