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. How many Calories are in a whole pepperoni pizza? How many Calories are in a whole ham-and-pineapple pizza?

Question

01-12-2020
Mathematics

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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. How many Calories are in a whole pepperoni pizza? How many Calories are in a whole ham-and-pineapple pizza?

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ngarcia6054 ngarcia6054 · Answer 1 · 2020-12-01T20:34:12+01:00

Answer:

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.