Half a pepperoni pizza plus three fourths a ham-and-pineapple pizza contains 765 calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 calories. How many calories are in each kind of pizza?

Let x be the number of calories in the pepperoni pizza and y be the number of calories in ham-and-pineapple pizza. Then, we can make two equations out of the problem statement.

Eq 1: (1/2) x + (3/4) y = 765

Eq 2: (1/4) x + y = 745

By transposing, Eq 2 becomes: y = 745 - (1/4) x. We substitute this to Eq. 1:

(1/2) x + (3/4) (745 - (1/4) x) = 765

x = 660

Then we substitute x to Eq 2 to get y:

y = 580

Thus, there is 660 calories in pepperoni pizza and 580 calories in ham-and-pineapple pizza.