Question

Casey orders three pizzas and two orders of breadsticks for a total of $28. Rachel orders two pizzas and three orders of breadsticks for a total of $22. How much does a pizza cost? How much does an order of breadsticks cost?

Answer 1

x=pizza, y=breadsticks

Casey: 3x+2y=28
Rachel: 2x+3y=22

from the first equation, y can also be expressed as (28-3x)/2. Thus Rachel = 2x + 3((28-3x)/2) = 22. Therefore, x=$8 per pizza and 2(8)+ 3y=22 ==> y=$2 per order of breadsticks

Answer 2

Let's create 2 equations out of the word problem, where P = pizza and B = breadsticks:
3P + 2B = 28
2P + 3B = 22

We have 2 variables, and 2 different equations so we can solve the problem with the information given.

There are many ways to solve a system of equations like this. One way is to substitute one equation into the other one. First, choose one of the variables, and multiply their respective equations to get to a common multiple.

For example, let's take P. Multiply BOTH SIDES of the top equation by 2, and multiply both sides of the bottom equation by 3 so that both equations will have 6P at the end.

2(3P + 2B) = 2*28 --> 6P + 4B = 56
3(2P + 3B) = 3*22 --> 6P + 9B = 66

Now, move the variables around in the top equation so that the 6P remains alone:
6P + 4B - 4B = 56 - 4B --> 6P = 56 - 4B

Substitute this equation you just made INTO the bottom equation.
6P + 9B = 66 --> (56 - 4B) + 9B = 66 --> 56 + 5B = 66 --> 5B = 10 --> B = 2

So now you know breadsticks cost $2, but what about pizza? simply substitute B into any one of the original equations.

3P + 2B = 28 --> 3P + 2(2) = 28 --> 3P + 4 = 28 --> 3P = 24 --> P = 8

So a pizza costs $8. Does that make sense?