need help with algebra

Question

one month deon rented 8 movies and 4 video games for a total of $33. The next month he rented 3 movies and 2 video games for a total of $15. find the rental cost for each movie and each video game.

Answer 1

Great question! Here is another way to do this question (as long as you are not afraid of large numbers!):

First, select two variables to represent your subjects of interest:

1. "m" = the number of movies
2. "v" = the number of video games

Next, create two equations using the numbers provided in the word problem:

1. 8 movies and 4 video games costs $33 --- 8m + 4v = 33
2. 3 movies and 2 video games cost $15 --- 3m + 2v = 15

Add the two equations together:

8m + 4v = 33

+ 3m + 2v = 15

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

11m + 6v = 48

Now, rewrite the new equation so that only one variable is on one side of the equation:

1. 11m + 6v = 48
2. 11m = 48 - 6v
3. m = (48 - 6v) / 11

Next, plug in the new value of variable "m" into one of the two equations created in Step #2. For example:

1. 3m + 2v = 15 becomes 3((48 - 6v)/11) + 2v = 15

Now, solve for variable "v".

1. First, distribute the "3" to the equation in parantheses:
2. 3((48 - 6v)/11) + 2v = 15
3. ((144 - 18v)/11) + 2v = 15
4. Next, multiple both sides of the equation by "11" in order to cancel out the denominator on the left sign of the equal sign.
5. 11 x ((144 - 18v)/11) + 2v) = 15 x 11
6. 144 - 18v + 22v = 165
7. Next, combine like terms:
8. -18v + 22v = 165 - 144
9. 4v = 21
10. Lastly, solve for "v" by dividing both sides of the equation by "4":
11. 4v / 4 = 21 / 4
12. v = 5.25

Now that we have the value for the variable "v", we can plug this number back into one of our equations in Step #2 to solve for the variable "m". For example:

1. 3m + 2v = 15
2. 3m + 2(5.25) = 15
3. 3m + 10.5 = 15
4. 3m = 15 - 10.5
5. 3m = 4.5
6. 3m / 3 = 4.5 / 3
7. m = 1.5

In conclusion, each movie costs $5.25 and each video game costs $1.50. If you have any questions then please let me know!

Answer 2

Let "m" represent the cost to rent one movie and let "v" represent the cost to rent one video game.

The 8 movies would cost 8 times the price of one movie or "8m" and 4 video games would cost "4v".Since "8 movies and 4 video games for a total of $33" then 8m + 4v = 33.

And likewise, 3m + 2v = 15

To make the "v's" get eliminated, we can multiply both sides of the second equation by -2 and it becomes:

-6m - 4v = -30

Then we can add the first equation to it:

8m + 4v = 33

-6m - 4v = -30

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

2m = 3

m = 1.5

Then we can plug in m = 1.5 into 3m + 2v = 15 to get:

3(1.5) + 2v = 15

4.5 + 2v = 15

2v = 10.5

v = 5.25

So each movie costs $1.50 and each video game costs $5.25 to rent