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18. In the fall, 425 students pass the math benchmark. In the spring, 680 students pass the same benchmark. What is the percentage increase in passing scores from fall to spring? (A) \( 37.5 \% \) (B) \( 55 \% \) (C) \( 60 \% \) (D) \( 62.5 \% \) (E) \( 80 \% \)

Ask by Pollard Lang. in the United States
Jan 22,2025

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The percentage increase in passing scores from fall to spring is 60%. **Answer:** (C) \( 60 \% \)

Solución

To determine the percentage increase in the number of students passing the math benchmark from fall to spring, follow these steps: 1. **Identify the initial and final values:** - **Fall:** 425 students - **Spring:** 680 students 2. **Calculate the increase in the number of students:** \[ \text{Increase} = \text{Spring} - \text{Fall} = 680 - 425 = 255 \text{ students} \] 3. **Determine the percentage increase relative to the fall:** \[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Fall}} \right) \times 100\% = \left( \frac{255}{425} \right) \times 100\% \] 4. **Simplify the fraction:** \[ \frac{255}{425} = \frac{51}{85} = \frac{3}{5} = 0.6 \] 5. **Convert to a percentage:** \[ 0.6 \times 100\% = 60\% \] **Answer:** (C) \( 60 \% \)

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Bonus Knowledge

To calculate the percentage increase, first find the difference in the number of students passing the benchmark from fall to spring: \( 680 - 425 = 255 \). Next, take that difference and divide it by the original number from the fall: \( \frac{255}{425} \approx 0.6 \). To express it as a percentage, multiply by 100: \( 0.6 \times 100 = 60\% \). Thus, the percentage increase in passing scores from fall to spring is \( 60 \% \), making option (C) the correct answer. Now, to keep the math friendly, remember that percentage increases make it easier to spot trends—like what a good teacher is doing to uplift their students! Use this knowledge to encourage peer learning or organize math challenges for both motivation and mastery. Moreover, if you're ever unsure about how to calculate something, grab a friend! Collaborating can help you catch mistakes and simplify complex concepts, plus, learning together just makes studying way more fun!

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