Question

One month Deandre rented 7 movies and 9 video games for a total of $78. The next month he rented 5 movies and 3 video games for a total of
$36. Find the rental cost for each movie and each video game.

Answer 1

Ok, you want to start by making two equations

Answer 2

For our equations, x will be movies and y will be games

Answer 3

First equation is 7x + 9y=78

Answer 4

Have any idea what the second will be?

Answer 5

@atlantaslast

Answer 6

5x+3y=36

Answer 7

Great! Now to solve we can use substitution, do you know how to use that?

Answer 8

Not that well.

Answer 9

That's fine, we'll work with the second one since it has smaller numbers.

Answer 10

So the basic idea is we will turn one equation into a value, that will substitute it's value in the other equation

Answer 11

that's a bunch of jibber jabber, but here is the math behind that statement

Answer 12

y=12-5x

Answer 13

Do you understand how I got to this from the original equation 5x+3y=36?

Answer 14

Nope!

Answer 15

wait did you multiply by 4?

Answer 16

Sorry I typed it wrong I meant to put y=12-5/3x

Answer 17

No, first I subtracted 5x from both sides, and then divide both sides by 3

Answer 18

the purpose is to isolate the y, have it on it's own

Answer 19

oh okay

Answer 20

So now that we have y=12-5/3x, we can plug it into the other equation

Answer 21

7x+9(12-5/3x)=78

Answer 22

Do you understand what I just did?

Answer 23

Yeah you plugged in the numbers to the equation

Answer 24

I found that the value of y is 12-5/3x, so I substituted y for 12-5/3x in the other equation

Answer 25

Now I want you to try to solve 7x+9(12-5/3x)=78 for x

Answer 26

7x+106.3=78 right?

Answer 27

No, we still don't know what x is.. so you would get 7x+108-15x=78

Answer 28

which becomes 108-8x=78

Answer 29

and then you subtract 8 from each side correct?

Answer 30

i mean add

Answer 31

not yet, first subtract 108 from each side, you need to isolate the x

Answer 32

so you get -8x=-30

Answer 33

now divide both sides by -8 and get x=15/4

Answer 34

yep, when you actually divide 15 by 4 you get 3.75 so every movie costs $3.75 to rent

Answer 35

now that we have that, we plug it into one of the originals, i'll use 5x+3y=36 since it's smaller numbers

Answer 36

plug in 3.75 for x... 5(3.75)+3y=36

Answer 37

and then you get 18.75+3y=36 right

Answer 38

yep, now subtract 18.75 from both sides

Answer 39

you should get 3y=17.25

Answer 40

yep i got that

Answer 41

divide both by 3 and get y=5.75

Answer 42

so every movie is $3.75, every game is $5.75

Answer 43

Thanks very much :)

Answer 44

no problem!