Answer
There are 660 calories in the whole pepperoni pizza and 580 calories in the whole ham and pineapple pizza.
Work Step by Step
The first step is to set up each equation with regard to the information given in the problem.
x=calories in pepperoni pizza and y= calories in ham and pineapple pizza.
1st: $\frac{1}{2}x + \frac{3}{4}y = 765$
2nd: $\frac{1}{4}x +y = 745 $
Using the multiplication strategy, we can multiply the 1st equation by 4 and 2nd equation by -8 to start the elimination process.
The first equation will become $2x+3y=3060$ and the second equation will become $-2x-8y=-5960$.
These two equations have the same coefficient for x with opposing signs. This means we can add them to eliminate.
$2x+3y=3060$ +
$-2x-8y=-5960$
After adding like terms we are left with $-5y = -2900 $. We then divide each side by -5 to get a result of $y=580$. We can substitute this into the equation $x+4y = 2980$. Solving for this equation $x+4(580) = 2980$ gives us a value of $2980-2320 = 660$
$x=660 $ and $ y= 580$
