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.