One month Ivanna rented 3 movies and 5 video games for a total of $37. The next month she rented 12 movies and 2 video games for a total of 31$ find the rental cost for each movie and each video game
3 m + 5 v = 37 ... 12 m + 20 v = 148
12 m + 2 v = 31
subtracting equations (to eliminate m) ... 18 v = 117
solve for v , then substitute back to find m
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 m and the rental cost for each video game is g.
According to the given information, we can write the following equations:
1) In the first month, Ivanna rented 3 movies and 5 video games for a total of $37:
3m + 5g = 37
2) In the next month, she rented 12 movies and 2 video games for a total of $31:
12m + 2g = 31
Now, we can solve this system of equations to find the values of m and g:
Multiplying the first equation by 2 and the second equation by 5 to eliminate g, we get:
6m + 10g = 74
10m + 2g = 31
Subtracting the second equation from the first equation, we have:
(6m + 10g) - (10m + 2g) = 74 - 31
6m + 10g - 10m - 2g = 43
-4m + 8g = 43
Simplifying further:
8g - 4m = 43
Now we can solve this equation for one variable and substitute it back into either equation 1 or 2 to find the other variable.
Let's solve the equation for m:
-4m = 43 - 8g
m = (43 - 8g) / -4
Now substitute this value of m in equation 1 or 2. Let's use equation 1 for simplicity:
3((43 - 8g) / -4) + 5g = 37
Multiply through by -4 to eliminate the fraction:
-12(43 - 8g) + 20g = -148
-516 + 96g + 20g = -148
116g = 368
g = 368 / 116
g = 3.17 (approximately)
Now substitute the value of g back into equation 1 or 2 to find m:
3m + 5(3.17) = 37
3m + 15.85 = 37
3m = 37 - 15.85
3m = 21.15
m = 21.15 / 3
m = 7.05 (approximately)
Therefore, the rental cost for each movie is approximately $7.05 and the rental cost for each video game is approximately $3.17.