The bakery sold a total of 80 cupcakes that day.
To find the total number of cupcakes sold, we can set up a proportion using the percent given.
Let x represent the total number of cupcakes sold.
The proportion is 76 is to x as 95 is to 100 (since 95% is the same as 95 out of 100).
This can be written as 76/x = 95/100.
We can cross multiply to solve for x. 100*76 = 95*x.
Simplifying, we get 7600 = 95x.
Dividing both sides by 95, we find that x = 80.
Therefore, the bakery sold a total of 80 cupcakes that day.