SOLUTION: A person was in charge of ordering 26 pizzas for the office party. He ordered three types of pizza: cheese, pepperoni, and supreme. The cheese pizzas cost $6 each, the pep
Algebra ->
Customizable Word Problem Solvers
-> Misc
-> SOLUTION: A person was in charge of ordering 26 pizzas for the office party. He ordered three types of pizza: cheese, pepperoni, and supreme. The cheese pizzas cost $6 each, the pep
Log On
Question 1138848: A person was in charge of ordering 26 pizzas for the office party. He ordered three types of pizza: cheese, pepperoni, and supreme. The cheese pizzas cost $6 each, the pepperoni pizzas cost $9 each, and the supreme pizzas cost $12 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If the person spent a total of $222 on pizza, how many pizzas of each type did he buy? Answer by greenestamps(13198) (Show Source):
c = # of cheese pizzas
p = # of pepperoni pizzas
s = # of supreme pizzas
the total number of pizzas was 26 the total cost was $222 the cost of the pepperoni pizzas was twice the cost of the cheese pizzas
There is an endless number of different paths for solving that system of 3 equations in 3 variables. The path I chose involved many twists and turns and was not particularly pleasant....
So instead of finishing the problem that way, let's spend a little effort to set up the problem using a single equation in a single variable and see if the resulting path to the solution is easier.
He spent twice as much on the $9 pepperoni pizzas as he spent on the $6 cheese pizzas:
Using this, we can let p=4x and c=3x; then 3p=4c=12x.
And then with p=4x and c=3x, and with 26 pizzas in all, the number of supreme pizzas is 26-7x.
With the two ways I chose to solve the problem, the little extra effort required to set up an equation using a single variable resulted in an equation that required far less effort to solve than the system of 3 equations in 3 variables.
While it is of course important to understand how to set up a problem like this with 3 variables directly from the given information, it is also important to know that very often the overall effort required to solve a problem will be greatly reduced if you can set up the problem using a single variable.
