SOLUTION: You are going to dinner and a hockey game, and you have two different plans as options. The family Pack provides 2 pizzas and 4 hockey tickets for $210. The Party Rock provides 4 p

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You are going to dinner and a hockey game, and you have two different plans as options. The family Pack provides 2 pizzas and 4 hockey tickets for $210. The Party Rock provides 4 p      Log On


   

Question 954277: You are going to dinner and a hockey game, and you have two different plans as options. The family Pack provides 2 pizzas and 4 hockey tickets for $210. The Party Rock provides 4 pizzas and 10 hockey tickets for $516. How much does one pizza cost and how much does one hockey ticket cost?
Variables
X=
Y=
System=
Solution=
Answer by aYummyNoodle(10) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the cost of a pizza
let y = the cost of a hockey ticket
We can now substitute the x and y in for the pizza and hockey tickets:
2x%2B4y=210 and
4x%2B10y=516
Of course, there are 3 different ways to solve systems of linear equations. They are graphing substitution, and elimination. For this system, I will use elimination.
We first multiply the first equation by 2 get both x's with the same coefficient:
4x%2B8y=420
4x%2B10y=516
Now that we both equations, we can subtract them from each other to eliminate the x. Subtracting the second equation from the first equation gives us
2y=94
Divide by 2 and then we get
y=47%7D%7D%0D%0ASo+a+hockey+ticket+costs+%2447%0D%0ANow+we+can+just+plug+the+%7B%7B%7By back into the original first equation to get:
2x%2B4%2847%29=210
2x%2B188=210
2x=22
x=11
So a pizza costs $11.
A pizza costs $11 and a hockey ticket costs $47.