Question
x + ≥ , where x is the amount Carlos earns each Saturday morning.
Carlos must earn at least $ each Saturday morning to have at least $200 in four
weeks.
A) Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and
he earns money each Saturday morning at his grandmother’s store. Write an inequality for the
amount of money Carlos will need to earn each Saturday morning, and describe the solutions.
Assume Carlos will earn the same amount each Saturday morning. (2 points)
Carlos must earn at least $ each Saturday morning to have at least $200 in four
weeks.
A) Carlos is hoping to save at least $200 in the next four weeks. His mom gives him $30, and
he earns money each Saturday morning at his grandmother’s store. Write an inequality for the
amount of money Carlos will need to earn each Saturday morning, and describe the solutions.
Assume Carlos will earn the same amount each Saturday morning. (2 points)
Answers
GPT-4o mini
Let's break down the scenario step by step.
1. **Define Variables:**
- Let \( x \) be the amount Carlos earns each Saturday morning.
- He has $30 from his mom.
2. **Total Savings Goal:**
- Carlos wants to save at least $200 in total over 4 weeks.
3. **Total Savings Equation:**
- Over 4 weeks, Carlos will earn \( 4x \) (since he earns \( x \) each Saturday).
- Therefore, the total amount of money Carlos will have after 4 weeks is:
\[
30 + 4x
\]
4. **Set Up the Inequality:**
- Carlos needs this total amount to be at least $200:
\[
30 + 4x \geq 200
\]
5. **Solve the Inequality:**
- To isolate \( 4x \), subtract 30 from both sides:
\[
4x \geq 200 - 30
\]
\[
4x \geq 170
\]
- Now, divide both sides by 4:
\[
x \geq \frac{170}{4}
\]
\[
x \geq 42.5
\]
6. **Conclusion:**
The inequality that describes how much Carlos needs to earn each Saturday morning is:
\[
x \geq 42.5
\]
**Description of Solutions:**
- The solutions to this inequality indicate that Carlos needs to earn **at least** $42.50 each Saturday morning. Any amount equal to or greater than $42.50 will allow Carlos to meet or exceed his savings goal of $200 in four weeks. If he earns less than this amount, he will not reach his goal.
1. **Define Variables:**
- Let \( x \) be the amount Carlos earns each Saturday morning.
- He has $30 from his mom.
2. **Total Savings Goal:**
- Carlos wants to save at least $200 in total over 4 weeks.
3. **Total Savings Equation:**
- Over 4 weeks, Carlos will earn \( 4x \) (since he earns \( x \) each Saturday).
- Therefore, the total amount of money Carlos will have after 4 weeks is:
\[
30 + 4x
\]
4. **Set Up the Inequality:**
- Carlos needs this total amount to be at least $200:
\[
30 + 4x \geq 200
\]
5. **Solve the Inequality:**
- To isolate \( 4x \), subtract 30 from both sides:
\[
4x \geq 200 - 30
\]
\[
4x \geq 170
\]
- Now, divide both sides by 4:
\[
x \geq \frac{170}{4}
\]
\[
x \geq 42.5
\]
6. **Conclusion:**
The inequality that describes how much Carlos needs to earn each Saturday morning is:
\[
x \geq 42.5
\]
**Description of Solutions:**
- The solutions to this inequality indicate that Carlos needs to earn **at least** $42.50 each Saturday morning. Any amount equal to or greater than $42.50 will allow Carlos to meet or exceed his savings goal of $200 in four weeks. If he earns less than this amount, he will not reach his goal.