To find the proportion that represents the wagon failures, we examine the data reported for both June and July.
In June, the failure rate was:
- 20 failures out of 500 wagons: \[ \frac{20}{500} \]
In July, the failure rate was:
- 25 failures out of 625 wagons: \[ \frac{25}{625} \]
To compare these two proportions, we look for an option that correctly sets these two ratios equal.
Let's analyze the options provided:
- \(\frac{25}{20} = \frac{500}{625}\) — This does not represent the failures and is incorrect.
- \(\frac{20}{25} = \frac{625}{500}\) — This is not relevant to the failures and is incorrect.
- \(\frac{20}{500} = \frac{625}{25}\) — This is incorrect because \(625 \div 25\) does not equal \(\frac{20}{500}\).
- \(\frac{20}{500} = \frac{25}{625}\) — This is correct. Both sides represent the failure rates from the two months. They can both be simplified to show that the proportions of failures are equivalent.
Thus, the proportion that can be used to represent the wagon failures is: \[ \frac{20}{500} = \frac{25}{625} \]
So the correct option is: \(\frac{20}{500} = \frac{25}{625}\).