# Christopher orders a 3 topping pizza for $15.25 and a 4 topping for $17 .75. Write and solve a system of linear equations to find the price of a plain cheese pizza (no toppings) and the cost of...

Christopher orders a 3 topping pizza for $15.25 and a 4 topping for $17 .75. Write and solve a system of linear equations to find the price of a plain cheese pizza (no toppings) and the cost of each topping.

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### 2 Answers

You accidentally left out the number of toppings from the second pizza but I assume it is 4 since it appears to be one higher by the price given. We are to find the price of a plain pizza and the cost of each topping. Let's let the price of a plain pizza be x and the cost of each individual topping be y. We can then write the following set of linear equations based on the information given:

x + 3y = 15.25

x + 4y = 17.75

If we multiply the top equation by -1 and then add the two equations algebraically, we can eliminate the x and solve for y:

-x - 3y = -15.25

x + 4y = 17.75

_______________

y = 2.50

So it appears that the cost of each topping (y) is $2.50. Now input this value into one of the original equations for solve for x:

x + 3(2.50) = 15.25

x + 7.50 = 15.25

x = 7.75

So it appears that the cost of a plain cheese pizza (x) is $7.75.

**Answer: Plain cheese pizza is $7.75. Each topping costs $2.50.**

The plain cheese pizza would cost $7.75, and from there, each topping would be an added $2.50.