Answer:
You would have to rent 28 movies.
Step-by-step explanation:
You would set up the problem as a system of equations. This means that you have to have two equations.
Dish: [tex]y=3.50x+40[/tex]
Direct TV: [tex]y=2.25x+75[/tex]
In order to find the answer to these, you can either graph them or set them equal to each other. If you graph them, the answer is where the two lines intersect. For this, we will set them equal to each other:
[tex]3.50x+40=2.25x+75[/tex]
To start, since there is a number with the same variable on both sides, we must subtract the lower one from both sides of the equation. In this case, we will subtract [tex]2.25x[/tex] from both sides, giving us:
[tex]1.25x+40=75[/tex]
Now, we solve like a normal two-step equation.
Subtract 40 from both sides:
[tex]1.25x=35[/tex]
After that, we will divide both sides of the equation by 1.25:
[tex]\frac{1.25x}{1.25}=\frac{35}{1.25}[/tex]
This gives us:
[tex]x=28[/tex]
Which means you would have to rent 28 movies exactly in order for their prices to match.
