Final answer:
The fraction of nails used is calculated by subtracting the final spring stretch from the initial spring stretch, then dividing by the initial stretch, resulting in a fraction of 2/5 or 40%. This indicates that 40% of the nails from the box have been used during the day.
Step-by-step explanation:
If the stretch of the spring is directly proportional to the weight of the nails, which is a common assumption in such scenarios, we can calculate the fraction of nails used based on the change in stretch of the spring. At the beginning of the day, the spring stretches 50 cm, and at the end of the day, it stretches 30 cm. This means that 20 cm of stretch is no longer being used.
Therefore, to calculate the fraction of nails used, you would subtract the final measurement from the initial measurement and then divide by the initial measurement:
Fraction used = (Initial stretch - Final stretch) / Initial stretch
Fraction used = (50 cm - 30 cm) / 50 cm = 20 cm / 50 cm = 2/5
To convert this fraction to a percentage, you multiply by 100:
Percentage used = (2/5) × 100 = 40%
So, 40% of the nails have been used throughout the day.