Can you help with my word problems

Question

Video Store A charges $9 to rent a video game for one week. Although only members can rent from the store, membership is free. Video Store B charges $4 to rent a video game for one week. Only members can rent from the store and membership is $50 per year. After how many video- game rentals will the total amount spent at each store be the same? What will be the total amount spent at each store

Answer 1

We have two stores which charge differently for video game rentals. Store A charges $9 per video game with no anuual fee. Store B charges $4 per video game with a $50 annual fee. We will come up with two equations to represent the total fee for both stores. 

 

Let y = total paid amount and x = the total video games rented.

 

Since store A has no annual fee and only charges $9 per video game, the equation then is:

 

                                                                                   y = 9x     (1)

 

Since store B has a $50 annual fee and charges $4 per video game, the equation is:

 

                                                                                   y = 4x+50   (2)

 

To find out how many video games you have to rent for the total amount spent to be the same for both stores, set the two equations equal to each other:

 

                                                                          9x = 4x+50

 

Now at this point solve for x (start by subtracting 4x to both sides):

 

                                                                         9x = 4x+50

                                                                       -4x     -4x

                                                                       ----------------

                                                                          5x=50

 

Now divide by 5 to both sides:

 

                                                                          5x/5=50/5

 

                                                                           x = 10

Since x represents the total amount of video games rented, we would have to rent 10 video games for the total amount spent at each store be the same. 

 

Now to find the total amount spent after 10 video game rentals, just plug in the value of x that we just found into equations (1) or (2) [they should both yield the same result]. I will choose equation (1) since it is simpler to work with:

 

                                                                          y=9x

                                                                          y=9(10)

                                                                          y=90

 

Since y represents the total pay amount, we would end up paying $90 in either store.

 

Thus, you would have to rent 10 video games for either store to charge you a fee of $90.

Answer 2

Store A charges 9x for x videos while store b charges 50+4x. To find out when you pay the same amount of money set 9x=4x+50

5x=50

X=10

 

For a total of 90 dollars spent.