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The total cost of 9 bags and 12 magazines is $108. The total cost of 4 magazines and 4 bags is $44. Find the cost of 1 bag.

Question

The total cost of 9 bags and 12 magazines is $108.

The total cost of 4 magazines and 4 bags is $44.
Find the cost of 1 bag.

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Solution

Let's denote the cost of one bag as B and the cost of one magazine as M.

From the problem, we have two equations:

  1. 9B + 12M = 108
  2. 4B + 4M = 44

We can simplify the second equation by dividing every term by 4, which gives us:

B + M = 11

Now we have a system of two equations, and we can solve it step by step.

First, let's express B from the second equation:

B = 11 - M

Now we can substitute B in the first equation:

9*(11 - M) + 12M = 108 99 - 9M + 12M = 108 3M = 9 M = 3

Substitute M = 3 into the equation B = 11 - M, we get:

B = 11 - 3 = 8

So, the cost of one bag is $8.

This problem has been solved

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