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.Com
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): You can put this solution on YOUR website!
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.
Then...
ANSWER:
cheese: 3x = 9
pepperoni: 4x = 12
supreme: 26-7x = 5
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.
RELATED QUESTIONS
A person was in charge of ordering 2626 pizzas for the office party. He ordered three... (answered by ikleyn)
Ben was in charge of ordering 35 pizzas for the office party. He ordered three types of... (answered by josmiceli)
Ben was in charge of ordering 35 pizzas for the office party. He ordered three types... (answered by richwmiller)
Ben was in charge of ordering 16 pizzas for the office party. He ordered three types... (answered by Boreal,jorel1380,stanbon,MathTherapy)
A person was in charge of ordering 35 pizzas for an office party. He ordered three types... (answered by TimothyLamb)
Ben was in charge of ordering 30 pizzas for the office party. He ordered three types of... (answered by stanbon)
Ben was in charge of ordering 32 pizzas for the office party. He ordered three types of... (answered by Fombitz,jorel555)
A person was in charge of ordering 38 pizzas for the office party. He ordered three types (answered by josgarithmetic)
Ben was in charge of ordering 35 pizzas for the office party. He ordered three types of... (answered by Fombitz)