Determine the number of each type that are rented that evening.

Revenues for a video rental store on a particular Friday evening are $867.50 for 310 rentals. The rental fee for movies is $3.00 each and the rental fee for a video game cartridge is $2.50 each. Determine the number of each type that are rented that evening.

call no of movies M andno of video game G

then, 3M + 2.5G = 867.50
and M + G = 310

I take it you have been doing simultaneous equations recently.

You can multiply 2nd equation by 3, to get 3M + 3G = 930 (Equation 3)
then subtract 1st equation from this, i.e. 3M in 3rd eqn minus 3M in 1st eqn, = 0M
and 3G in 3rd eqn minus 2.5G in 1st eqn = 1/2 G
and on other side, 930 - 867.5 = 62.5

which gives 1/2 G = 62.5
so G = 125.

but as you know that M + G = 310,
it follows that M = 310 - 125
so M = 185

I hope you can follow this and not just copy down without digesting.

Let x = number of movies
Let y = number of video games

310 = x + y

Which means:

x = 310 - y

So plug this into our other equation where there is an x:

867.5 = 3x + 2.5y

867.5 = 3(310-y) + 2.5y

867.5 = 930 - 3y + 2.5y

867.5 - 930 = -0.5y

-32.5 = -0.5y

65 = y

Now plug this into your equation for x:

x = 310 - y

x = 310 - 65

x = 245

So, 245 movies and 65 video games.