One month Ivanna rented 5 movies and 3 video games for a total of $29. The next month she rented 2 movies and 12 video games for a total of $71. Find the rental cost for each movie and each video game.
Rental cost for each movie?
Rental cost for each video?
5m+3v = 29
2m+12v = 71
or
20m+12v = 116
2m+12v = 71
18m = 45
m = 2.50
v = 5.50
To find the rental cost for each movie and each video game, we can set up a system of equations.
Let's assume the rental cost for each movie is x dollars, and the rental cost for each video game is y dollars.
From the first month's rental, we know that Ivanna rented 5 movies and 3 video games for a total of $29. Therefore, we can write the equation:
5x + 3y = 29
From the second month's rental, we know that Ivanna rented 2 movies and 12 video games for a total of $71. Therefore, we can write the equation:
2x + 12y = 71
Now, we have a system of equations:
5x + 3y = 29
2x + 12y = 71
To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution. Rearrange the first equation for x:
5x = 29 - 3y
x = (29 - 3y) / 5
Now substitute this expression for x in the second equation:
2((29 - 3y) / 5) + 12y = 71
Simplify:
(58 - 6y)/5 + 12y = 71
Multiply through by 5 to get rid of the fraction:
58 - 6y + 60y = 355
Combine like terms:
54y = 297
Divide both sides by 54:
y = 297/54
y = 5.5
Now substitute this value of y back into the first equation to find x:
5x + 3(5.5) = 29
5x + 16.5 = 29
5x = 29 - 16.5
5x = 12.5
x = 12.5 / 5
x = 2.5
So, the rental cost for each movie is $2.5, and the rental cost for each video game is $5.5.