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strojnjashka [21]
3 years ago
7

Half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories 1/4 of a pepperoni pizza plus a who

le ham and pineapple pizza contains 745 calories how many calories are in a whole pepperoni pizza and how many calories are in a whole ham and pineapple pizza
a) 600 calories, 550 calories
b) 480 calories, 640 calories
c) 520 calories, 680 calories
d) 660 calories, 580 calories
Mathematics
1 answer:
yulyashka [42]3 years ago
6 0

Answer:

Correct choice is D (In a whole pepperoni pizza are 660 calories, in  in a whole ham and pineapple pizza are 580 calories).

Step-by-step explanation:

Let x calories be the number of calories a whole pepperoni pizza contains and y calories be the number of calories a whole ham and pineapple pizza contains.

1. If half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories, then

\dfrac{1}{2}x+\dfrac{3}{4}y=765.

2. If 1/4 of a pepperoni pizza plus a whole ham and pineapple pizza contains 745 calories. then

\dfrac{1}{4}x+y=745.

3. Multiply each equation by 4 and get a system of two equations:

\left\{\begin{array}{l}2x+3y=3060\\x+4y=2980\end{array}\right.

From the second equation x=2980-4y, then

2(2980-4y)+3y=3060,\\ \\5960-8y+3y=3060,\\ \\-8y+3y=3060-5960,\\ \\-5y=-2900,\\ \\y=580.

Then

x=2980-4\cdot 580=2980-2320=660.

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