Here is the problem:
Christopher orders a three topping pizza for $15.25, and a 5 topping pizza 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.
I used the method of elimination to get the answer, "Each pizza topping is $1.15.
When I placed 1.15 into each equation ( 3x + y = 15.25 and 5x + y = 17.75) to get the cost a a plain cheese pizza, I got 11.8 for the first equation and 12 for the second. That's confusing.
I concluded that Each pizza topping is $1.15, and each plain pizza is $12. Is this correct?
x = amount per topping
b = base price for cheese
15.25 = b + 3 x
17.75 = b + 5 x
----------------subtract
-2.5 = -2x
x = 1.25 Not 1.15 I think
17.75 = b + 5 (1.25)
b = 11.50
Thank you very much.
To solve this problem, you correctly set up a system of linear equations to find the price of a plain cheese pizza and the cost of each topping.
Let's call the price of a plain cheese pizza "x" and the cost of each topping "y".
Now, we can set up two equations based on the given information:
Equation 1: 3x + y = 15.25 (price of a three topping pizza)
Equation 2: 5x + y = 17.75 (price of a five topping pizza)
To solve this system of equations, you used the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
In this case, if we subtract Equation 1 from Equation 2, we can eliminate "y":
(5x + y) - (3x + y) = 17.75 - 15.25
5x - 3x + y - y = 2.5
Simplifying this equation, we get:
2x = 2.5
Dividing both sides by 2, we find:
x = 1.25
So, the price of a plain cheese pizza (no toppings) is $1.25.
Now, to find the cost of each topping, we can substitute this value of x back into one of the equations.
Let's substitute x = 1.25 into Equation 1:
3(1.25) + y = 15.25
3.75 + y = 15.25
Subtracting 3.75 from both sides, we get:
y = 11.5
So, the cost of each topping is $11.5.
Based on this solution, it appears that there might be a calculation error in your conclusion. The correct answer is that each pizza topping is $11.5, and the cost of a plain cheese pizza is $1.25.