Question
Which equation does NOT represent its situation? (1 point)
y = 22.5x + 150 James eams $22.50 per hour as a freelance graphic designer. He received an initial setup fee of $150 from his first client.
y = 12x + 50 Emma charges $12 per hour for walking dogs. A customer paid her an additional $50 tip upfront for excellent service.
y = 75x + 30 Sophia tutors students at a rate of $30 per hour. She also received a one-time sign-up bonus of $75 from the tutoring platform.
y = 15.8x + 200 Liam works for a delivery service that pays him $15.80 per hour. He also received a starting bonus of $200.
y = 22.5x + 150 James eams $22.50 per hour as a freelance graphic designer. He received an initial setup fee of $150 from his first client.
y = 12x + 50 Emma charges $12 per hour for walking dogs. A customer paid her an additional $50 tip upfront for excellent service.
y = 75x + 30 Sophia tutors students at a rate of $30 per hour. She also received a one-time sign-up bonus of $75 from the tutoring platform.
y = 15.8x + 200 Liam works for a delivery service that pays him $15.80 per hour. He also received a starting bonus of $200.
Answers
GPT-4o mini
To determine which equation does NOT correctly represent its situation, we can evaluate the information provided in each case:
1. **James**:
\[ y = 22.5x + 150 \]
- $22.50 per hour (variable part) and a setup fee of $150 (fixed part). This equation is correct.
2. **Emma**:
\[ y = 12x + 50 \]
- $12 per hour (variable part) and a tip of $50 (fixed part). This equation is also correct.
3. **Sophia**:
\[ y = 75x + 30 \]
- Rate of $30 per hour (variable part) and a sign-up bonus of $75 (fixed part). However, the amount of $75 should be added to the fixed part, meaning it should be:
\[ y = 30x + 75 \]
This equation is incorrect.
4. **Liam**:
\[ y = 15.8x + 200 \]
- $15.80 per hour (variable part) and a starting bonus of $200 (fixed part). This equation is correct.
Thus, the equation that does NOT represent its situation correctly is:
**y = 75x + 30 (Sophia's equation).**
1. **James**:
\[ y = 22.5x + 150 \]
- $22.50 per hour (variable part) and a setup fee of $150 (fixed part). This equation is correct.
2. **Emma**:
\[ y = 12x + 50 \]
- $12 per hour (variable part) and a tip of $50 (fixed part). This equation is also correct.
3. **Sophia**:
\[ y = 75x + 30 \]
- Rate of $30 per hour (variable part) and a sign-up bonus of $75 (fixed part). However, the amount of $75 should be added to the fixed part, meaning it should be:
\[ y = 30x + 75 \]
This equation is incorrect.
4. **Liam**:
\[ y = 15.8x + 200 \]
- $15.80 per hour (variable part) and a starting bonus of $200 (fixed part). This equation is correct.
Thus, the equation that does NOT represent its situation correctly is:
**y = 75x + 30 (Sophia's equation).**