Question

Ashley rented some movies and video games last month.She did the same this month.The table below shows the number of video games she rented each month.it also shows the total cost(in dollars).Let x be the cost of renting a movie.Let y be the cost of renting a video game.How much did it cost to rent each movie and each video game?

Answer 1

EXPLANATION

Let's see the facts:

x= cost of renting a movie

y= cost of renting a video game

Total cost = x*Number of movies + y*Number of video games

As we can see from the table:

Total cost Last month---->

(1) 32 = 5x + 3y

Total cost This month--->

(2) 83 = 2x + 12y

We have a system of equations and can solve it by substitution method:

Isolating x in (1) by subtracting -3y to both sides:

32 - 3y = 5x

Dividing both sides by 5:

32/5 -3y/5 = x

Switching:

x= (-3/5)y+32/5

Subtituting x in (2):

83 = 2[(-3/5)y+32/5]+12y (Applying distributive property)

83 = (-2*3/5)y + (2*32/5) +12y (Simplifying)

83 = (-6/5)y +12y +64/5 (Adding similar terms)

83 = (54/5)y + 64/5 (Subtracting -64/5 to both sides)

83 - 64/5 = (54/5)y

351/5 = (54/5)y (Multipliying both sides by 5/54)

(351/5)*(5/54)= y (Simplifying)

13/2 = y (Switching)

y=13/2

Now, replacing y=13/2 in x=(-3/5)y+32/5

x= (-3/5)*(13/2) + 32/5

x = 5/2

So,

Cost of renting a movie------------> x=5/2= 2.5 dollars

Cost of renting a video game----> y=13/2=6.5 dollars

Answer:

It cost 2.5 dollars to rent each movie and 6.5 dollars to rent each video game.