Half a pepperoni pizza plus three fourths of a ham-and-pineapple pizza contains 765 calories. One fourth of a pepperoni pizza plus a whole ham-and-pineapple pizza contains 745 calories. Write and solve a system of equations to determine how many calories are in a whole pepperoni pizza and how many calories are in a whole ham-and-pineapple pizza.
Let's represent the number of calories in a whole pepperoni pizza as P and the number of calories in a whole ham-and-pineapple pizza as H.
From the given information, we can set up the following system of equations:
(1/2)P + (3/4)H = 765
(1/4)P + H = 745
To solve this system, we can first multiply both sides of the second equation by 4 to eliminate the fractions:
P + 4H = 2980
We can then multiply the first equation by 4 to make the coefficients of P in both equations equal:
2P + 3H = 3060
Now we have a system of equations:
2P + 3H = 3060
P + 4H = 2980
We can solve this system by either eliminating one variable or solving through substitution.
Let's solve through elimination. Multiply the second equation by 2:
2P + 8H = 5960
Subtract this equation from the first equation:
2P + 3H - (2P + 8H) = 3060 - 5960
-5H = -2900
H = -2900 / -5
H = 580
Substitute the value of H back into the second equation to find P:
P + 4(580) = 2980
P + 2320 = 2980
P = 2980 - 2320
P = 660
Therefore, a whole pepperoni pizza contains 660 calories and a whole ham-and-pineapple pizza contains 580 calories.