Algebra Word problem

Question

One month Kevin rented 12 movies and 2 video games for a total of $41 .

The next month he rented 3 movies and 5 video games for a total of $35.

Find the rental cost for each movie and each video game.

Answer 1

m = movie rental rate; v = video game rental rate..

For 1st month: 12m + 2v = $41

For 2nd month: 3m + 5v = $35

Need to eliminate one of the variables. Easiest to to multiply 2nd equation by -4 to eliminate the "m".

12m + 2v = 41

-12m - 20v = -140

-18v = -99

v = -99/-18 = $5.50

Then 3m +5(5.50) = 35

3m + 27.50 = 35

3m = 7.50

m = 7.50/3 = $2.50

Check: 12(2.50) + 2(5.50) = 30 + 11 = 41

Also 3(2.50) + 5(5.50) = 7.50 + 27.50 = 35

Answer 2

Let M = cost in dollars to rent one movie.

Let V = cost in dollars to rent one video game.

12M + 2V = 41 equation 1

3M + 5V = 35 equation 2

I will multiply the 2nd equation by -4 to eliminate the variable M.

12M + 2V = 41

-12M - 20V = -140

-18V = -99

V = 5.50

Now use equation 1 to find M. Then check with equation 2. (You cause either of the original equations to find the 2nd variable. Just be sure to check your final answer using the other equation.)

12M + 2(5.50) = 41

12M + 11 = 41

12M = 30

M = 2.50

Now to check

3(2.50) + 5(5.50) = 35

7.50 + 27.50 = 35

35 = 35 check

It costs $2.50 to rent a movie and $5.50 to rent a video game.