To determine who was closer to their respective state records, we need to perform the following calculations:
- Convert all measurements to the same unit. We'll convert everything to feet.
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Alex's Jump: 39.75 feet (already in feet)
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Eric's Jump: \( 37 \text{ feet} \) and \( 1 \frac{1}{4} \text{ inches} \)
First, convert \( 1 \frac{1}{4} \text{ inches} \) to feet: \[ 1 \frac{1}{4} = \frac{5}{4} \text{ inches} = \frac{5}{4} \div 12 = \frac{5}{48} \text{ feet} \]
Therefore, Eric's jump in feet is: \[ 37 + \frac{5}{48} = \frac{37 \times 48}{48} + \frac{5}{48} = \frac{1776 + 5}{48} = \frac{1781}{48} \approx 37.52 \text{ feet} \]
- Determine the state records in feet as well:
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Eighth Grade Record: 42.25 feet (already in feet)
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Seventh Grade Record: \( 39 \text{ feet} \) and \( 3 \text{ inches} \)
Convert \( 3 \text{ inches} \) to feet: \[ 3 \text{ inches} = \frac{3}{12} = \frac{1}{4} \text{ feet} \]
Therefore, the seventh-grade record in feet is: \[ 39 + \frac{1}{4} = 39.25 \text{ feet} \]
- Calculate the differences between the jumps and the records:
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Alex's difference from the eighth-grade record: \[ 42.25 - 39.75 = 2.50 \text{ feet} \]
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Eric's difference from the seventh-grade record: \[ 39.25 - 37.52 \approx 1.73 \text{ feet} \]
- Compare the differences:
- Alex was 2.50 feet away from the eighth-grade record.
- Eric was approximately 1.73 feet away from the seventh-grade record.
Conclusion: Eric was closer to his state record than Alex was to his.
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