Question

Mr. O'Hara ordered a total of 8 pizzas to celebrate the end of the soccer season. If Mr. O'Hara ordered 2 more cheese pizzas than pepperoni pizzas, how many of each type did he order?​

Answer 1

Answer:

5 cheese pizzas and 3 pepperoni pizzas

Step-by-step explanation:

The correct way to solve this is to formulate two related equations since there are two unknowns...the number or pepperoni pizzas and the number of cheese pizzas.

To make is easier to write...we will call pepperoni pizzas p and cheese pizzas c.

we know that the total number of pizzas is 8 so

p + c = 8

Pepperoni (p) pizzas plus Cheese (c) pizzas is 8

We also know that

c = p + 2

Cheese (c) pizzas is equal to Pepperoni (p) pizzas plus 2...there are two more cheese pizzas than pepperoni pizzas.

if we use this second equation to replace for c in the first equation we get

p + (p +2) = 8

c and (p + 2) are the same value so we can use either in place of the other. I am using the parentheses just to group p plus 2 together to hopefully make it clear what I did.

If we now add the two p together we get 2p so the equation is now

2p + 2 = 8

If we now subtract 2 from both sides we maintain the equality because we are making the same change to both sides

2p + 2 - 2 = 8 - 2

2 minus 2 is zero and 8 minus 2 is 6

2p = 6

Now if we divide both sides by 2 we get the following

p = 3

This is because 2p divided by 2 is 1p or just p and 6 divided by 2 is 3.

This tells us that there are 3 pepperoni pizzas as p stands for pepperoni here

Now if we go back to either equation and substitute the value 3 for the variable p we can solve for c or cheese pizzas

c = p + 2 was one equation so

c = 3 + 2

or

c = 5

if we use the other equation, p + c = 8 we get

3 + c = 8

We can subtract 3 from both sides and maintain the equality

3 - 3 + c = 8 - 3

3 minus 3 is zero and 8 minus 3 is 5 so again

c = 5

There are 3 pepperoni pizzas and 5 cheese pizzas

Answer 2

She ordered 6 pepperoni pizzas and 2 cheese pizzas