John Anderson knows that the pizza pipeline charges its customers a certain amount per one topping pizza, plus a fixed price for delivery. The checks that John wrote for the last two deliveries were $17 for two pizzas and $31 for four pizzas. How much would each pizza cost without delivery, how much is the fixed delivery charge, and how much wood five pizzas cost with delivery
If the fixed cost is f and the per-pizza cost is p, then we know:
c+2p = 17
c+4p = 31
now subtract and you see that
2p = 14
now you can find p, and then c.
The five pizzas cost c+5p
To determine the cost of each pizza without delivery and the fixed delivery charge, we can set up a system of equations based on the given information.
Let's assume the cost of each pizza without delivery is 'x', and the fixed delivery charge is 'y'.
From the given information:
- For the first check ($17 for two pizzas), we can write the equation as: 2x + y = 17.
- For the second check ($31 for four pizzas), the equation can be expressed as: 4x + y = 31.
Now, we have a system of equations:
Eq1: 2x + y = 17
Eq2: 4x + y = 31
To solve this system of equations, we can use the method of substitution or elimination.
Using the method of elimination:
- Multiply Eq1 by 2 to eliminate the 'y' term:
2(2x + y) = 2(17)
4x + 2y = 34
- Subtract Eq2 from the above equation to eliminate the 'y' term:
(4x + 2y) - (4x + y) = 34 - 31
4x + 2y - 4x - y = 3y = 3
- Divide both sides of the equation by 3 to solve for 'y':
3y/3 = 3/3
y = 1
Now, we have found the fixed delivery charge, y, which is $1.
To find the cost of each pizza without delivery, we can substitute the value of y = 1 into Eq1:
2x + 1 = 17
2x = 17 - 1
2x = 16
x = 16/2
x = 8
Therefore, the cost of each pizza without delivery is $8.
Now, let's find out how much five pizzas would cost with delivery:
Cost of 5 pizzas with delivery = (Cost of each pizza without delivery * Number of pizzas) + Fixed delivery charge
= ($8 * 5) + $1
= $40 + $1
= $41
Hence, five pizzas with delivery would cost $41.