Answer: Let's assume the rental cost for each movie is M and the rental cost for each video game is G. Then we can set up a system of two equations based on the given information:
3M + 8G = 53 (equation 1)
5M + 2G = 26 (equation 2)
We can use any method to solve this system of equations, but let's use the elimination method by multiplying equation 1 by 2 and subtracting it from equation 2:
10M + 4G = 52 (multiplying equation 1 by 2)
(3M + 8G = 53) (subtracting equation 1 from equation 2)
7M - 4G = -1 (resulting equation)
Now we can solve for one variable in terms of the other. Let's solve for M:
7M - 4G = -1
7M = 4G - 1
M = (4G - 1)/7
We can substitute this expression for M into either equation 1 or equation 2 to solve for G. Let's use equation 2:
5M + 2G = 26
5[(4G - 1)/7] + 2G = 26 (substituting for M)
(20G - 5)/7 + 2G = 26
20G - 5 + 14G = 182 (multiplying both sides by 7 to eliminate the denominator)
34G = 187
G = 187/34
Now we can substitute this value for G into the expression we found for M to get:
M = (4(187/34) - 1)/7 = 3.5
Therefore, the rental cost for each movie is $3.50, and the rental cost for each video game is approximately $5.50 (rounded to the nearest cent).
To check our solution, we can verify that it satisfies both equations:
3(3.5) + 8(5.5) = 53 (first month rental cost)
5(3.5) + 2(5.5) = 26 (second month rental cost)
Both equations are satisfied, so we can be confident in our solution.
Explanation: