Question
3. In a basketball game, Glenn scored \( 25 \% \) more points than Ry, If \( g \) is the number of roints that Qlenn scored and \( r \) is the number of points that FJ seored, whioh equatione re correct? Select all that apply. A) \( g=r+25 \) B) \( g=r+.25 r \) C) \( g=r+.25 \) () \( g=1.25 r \) () \( g=(1+.25) r \)
Ask by Reid Romero. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The correct equations are:
- B) \( g = r + 0.25r \)
- D) \( g = 1.25r \)
- E) \( g = (1 + 0.25)r \)
Solution
To determine which equations correctly represent the relationship where **Glenn scored 25% more points than Ry**, let's analyze each option step by step.
### Given:
- Let \( g \) = points scored by Glenn
- Let \( r \) = points scored by Ry
### Interpretation:
"Glenn scored 25% more points than Ry" translates to:
\[ g = r + 25\% \text{ of } r \]
\[ g = r + 0.25r \]
\[ g = 1.25r \]
\[ g = (1 + 0.25)r \]
### Evaluating Each Option:
**A) \( g = r + 25 \)**
- **Interpretation:** Glenn scored **25 more points** than Ry.
- **Analysis:** This implies a fixed increase of 25 points, not a percentage increase.
- **Conclusion:** **Incorrect**
**B) \( g = r + 0.25r \)**
- **Interpretation:** Glenn scored **\( r \) plus 25% of \( r \)**.
- **Analysis:** This accurately represents a 25% increase.
- **Conclusion:** **Correct**
**C) \( g = r + 0.25 \)**
- **Interpretation:** Glenn scored **\( r \) plus 0.25 points**.
- **Analysis:** This implies a fixed increase of 0.25 points, not a percentage.
- **Conclusion:** **Incorrect**
**D) \( g = 1.25r \)**
- **Interpretation:** Glenn scored **1.25 times what Ry scored**.
- **Analysis:** Multiplying by 1.25 correctly represents a 25% increase.
- **Conclusion:** **Correct**
**E) \( g = (1 + 0.25)r \)**
- **Interpretation:** Glenn scored **\( 1 + 0.25 \) times \( r \)**.
- **Analysis:** Simplifies to \( g = 1.25r \), which is correct.
- **Conclusion:** **Correct**
### **Correct Equations:**
- **B) \( g = r + 0.25r \)**
- **D) \( g = 1.25r \)**
- **E) \( g = (1 + 0.25)r \)**
These three equations accurately represent that Glenn scored 25% more points than Ry.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Glenn's scoring at \( 25\% \) more points than Ry means he scored \( 1.25 \) times what Ry did. This results from multiplying Ry's score by \( 1 + 0.25 \) (the original score plus \( 25\% \)). Hence, \( g = 1.25 r \) and \( g = (1 + 0.25) r \) are the correct equations. In real life, understanding percentage increases is not just useful in sports, but also in finance, sales, and various fields. For example, if a product's sales increase by \( 25\% \), you’d look at the previous sales figures and multiply by \( 1.25 \) to find the new sales total. This concept helps in making sense of growth models in economic trends too!
