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? (1 point) Responses 600 Calories, 550 Calories 600 Calories, 550 Calories 480 Calories, 640 Calories 480 Calories, 640 Calories 520 Calories, 680 Calories 520 Calories, 680 Calories 660 Calories, 580 Calories
Let's say the number of calories in a whole pepperoni pizza is x and the number of calories in a whole ham-and-pineapple pizza is y.
From the given information, we can set up the following equations:
(1/2)x + (3/4)y = 765 (equation 1)
(1/4)x + y = 745 (equation 2)
To solve the system of equations, we can multiply equation 2 by 4 to eliminate the fractions:
4 * ((1/4)x + y) = 4 * 745
x + 4y = 2980 (equation 3)
Now we can solve equations 1 and 3 simultaneously:
(1/2)x + (3/4)y = 765 (equation 1)
x + 4y = 2980 (equation 3)
Multiply equation 1 by 4 to eliminate the fractions:
4 * ((1/2)x + (3/4)y) = 4 * 765
2x + 3y = 3060 (equation 4)
Now we have the following system of linear equations:
x + 4y = 2980 (equation 3)
2x + 3y = 3060 (equation 4)
Using substitution method, we can solve for x:
Multiply equation 3 by 2:
2 * (x + 4y) = 2 * 2980
2x + 8y = 5960
Subtract equation 4 from the above equation:
(2x + 8y) - (2x + 3y) = 5960 - 3060
5y = 2900
y = 2900/5
y = 580
Now we can substitute the value of y into equation 3 to solve for x:
x + 4(580) = 2980
x + 2320 = 2980
x = 2980 - 2320
x = 660
So, a whole pepperoni pizza contains 660 Calories and a whole ham-and-pineapple pizza contains 580 Calories.
Therefore, the correct answer is:
660 Calories, 580 Calories