Newcastle East Public School is having a cupcake sale to raise money for a local charity. They have 250 cupcakes to sell. Of these, 15 are chocolate and the remainder are vanilla. At the end of the day, 2425 of the chocolate cupcakes were sold, and overall 710 of all the cupcakes sold. What fraction of vanilla cupcakes were sold on the day?

First, let's determine the number of vanilla cupcakes. We know there are 250 cupcakes in total and 15 of them are chocolate. Therefore, the number of vanilla cupcakes is:

250 - 15 = 235

Next, we need to find out how many chocolate cupcakes were sold. According to the information given, 2425 of the chocolate cupcakes were sold. Since there are only 15 chocolate cupcakes, it seems there might be a typo. Assuming it meant 24 out of 25 chocolate cupcakes were sold, we can calculate:

24/25 * 15 = 14.4

Since we can't sell a fraction of a cupcake, we assume 14 chocolate cupcakes were sold.

Now, we need to find out how many cupcakes were sold in total. According to the information, 710 of all the cupcakes were sold. Therefore:

710 * 250 = 175 cupcakes sold in total

To find out how many vanilla cupcakes were sold, we subtract the number of chocolate cupcakes sold from the total number of cupcakes sold:

175 - 14 = 161 vanilla cupcakes sold

Finally, we calculate the fraction of vanilla cupcakes sold:

161 / 235

To simplify this fraction, we find the greatest common divisor (GCD) of 161 and 235, which is 1. Therefore, the fraction of vanilla cupcakes sold is:

161 / 235