SOLUTION: stion One month Alonzo rented 2 movies and 3 video games for a total of $ 24 . The next month he rented 4 movies and 8 video games for a total of $

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: stion One month Alonzo rented 2 movies and 3 video games for a total of $ 24 . The next month he rented 4 movies and 8 video games for a total of $      Log On


   

Question 1154041: stion

One month Alonzo rented
2
movies and
3
video games for a total of
$
24
. The next month he rented
4
movies and
8
video games for a total of
$
61
. Find the rental cost for each movie and each video game.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let movies be m and video games v
if one month Alonzo rented 2 movies and 3 video games for a total of $24, we have
2m%2B3v=24 ......solve for m
2m=24-3v
m=12-3v%2F2........eq.1


if the next month he rented 4 movies and 8 video games for a total of $61, we have
4m%2B8v=61 ......solve for m
4m=61-8v
m=61%2F4-2v........eq.2

from eq.1 and eq.2 we have

12-3v%2F2=61%2F4-2v.....solve for v
12-61%2F4=3v%2F2-2v
48%2F4-61%2F4=3v%2F2-4v%2F2
-13%2F4=-v%2F2.....switch sides
v%2F2=13%2F4
v=2%2813%2F4%29
v=%2813%2F2%29
v=6.50

go to
m=12-3v%2F2........eq.1, substitute v
m=12-%283%2A6.50%29%2F2
m=12-9.75
m=2.25

=> the rental cost for each movie is $2.25 and each video game is $6.50


Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

stion
One month Alonzo rented
2
movies and
3
video games for a total of
$
24
. The next month he rented
4
movies and
8
video games for a total of
$
61
. Find the rental cost for each movie and each video game. 
Let the cost of a movie and a video game be M, and V, respectively

Then we get: 2M + 3V = 24 ------- eq (i)

Also, 4M + 8V = 61 ------ eq (ii)

- 4M - 6V = - 48 -------- Multiplying eq (i) by - 2 ------ eq (iii)

2V = 13 ------ Adding eq (iii) & eq (ii)

V, or cost of a video game = highlight_green%28matrix%281%2C3%2C+13%2F2%2C+%22=%22%2C+%22%246.50%22%29%29

Substitute 6.5 for V in either eq (i) or (ii) to find the cost of a movie.

That's it!! Nothing as complex as the other person makes it seem.