Answer:
cost of each video game = $5.50
cost of each movie = $4.25.
Step-by-step explanation:
Let m represent cost per movie
g represents cost per video game.
Create two equations to represent the total cost Tammy rented movie and video games in each month, and solve simultaneously for each variable:
First month:
[tex] 2m + 3g = 25 [/tex] => equation 1
Second month:
[tex] 4m + 8g = 61 [/tex] => equation 2
Multiply equation 1 by 4, and multiply equation 2 by 2 to derive:
4 × [tex] 2m + 3g = 25 [/tex]
2 × [tex] 4m + 8g = 61 [/tex]
[tex] 8m + 12g = 100 [/tex] => equation 3
[tex] 8m + 16g = 122 [/tex] => equation 4
Subtract equation 4 from equation 3
You'd have:
- 4g = - 22
Divide both sides by -4
g = 5.5
Thus, the cost of each video game = $5.50.
Substitute g = 5.5 in equation 1 and solve for m.
[tex] 2m + 3g = 25 [/tex]
[tex] 2m + 3(5.5) = 25 [/tex]
[tex] 2m + 16.5 = 25 [/tex]
Subtract 16.5 from each side
[tex] 2m = 25 - 16.5 [/tex]
[tex] 2m = 8.5 [/tex]
Divide both sides by 2
[tex] m = 4.25 [/tex]
Thus, cost of each movie = $4.25.
