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One month Ravi rented 3 movies and 8 video games for a total of $53. The next month he rented 5 movies and 2 video games for a total of $26. Find the rental cost for each movie and each video game.

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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:

User Guenther Schmitz
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