Answer:
A movie is $2.5
A video game is $6
Explanation:
Pre-Solving
We are given that Ann had rented 2 movies and 5 video games for a total of $35.
We also know that she also rented 8 movies and 3 video games for a total of $38.
We want to know how much a movie costs, and how much a video game costs.
If a movie costs x dollars, then a video game costs y dollars.
Solving
This means that costwise, 2 movies will cost 2x, and 5 video games will be 5y.
8 movies will cost 8x, and 3 video games will cost 3y.
So, we will have two equations:
2x + 5y = 35
8x + 3y = 38
We now have this system of equations, which we can solve.
Let's solve this by elimination.
To eliminate, we need to clear one of the variables, and solve for the other one.
To do this, we need to make sure that one variable has the same coefficient with opposite signs (e.g. -3x and 3x). We might need to multiply one equation by a number in order to achieve this.
We can multiply 2x + 5y = 35 by -4.
-4(2x + 5y) = -4(35)
-8x - 20y = -140
We can rewrite the equations:
-8x - 20y = -140
8x + 3y = 38
They can be added together. The result will be:
-17y = -102
Divide both sides by 017.
y = 6
We found y, but now we need to find x.
We can substitute 6 as y into 2x + 5y = 35 or 8x + 3y = 38 to find x.
Taking 2x + 5y = 35 for instance:
2x + 5(6) = 35
2x + 30 = 35
Subtract 30 from both sides.
2x = 5
Divide both sides by 2
x = 2.5
Recall that x = price of a movie, and y = price of a video game.
Therefore, a movie is 2.5 dollars, and a video game is 6 dollars.