The total cost of each company can be calculated by adding the monthly fee and the cost of the calls, then we can formulate the following expression:
Total cost = monthly fee + cost for calls
Company A has a monthly fee of $20, then we can rewrite the above equation like this:
Cost company A = 20 + cost for calls
The cost for calls can be calculated by multiplying the fee per minute and the calling minutes, by calling x to the calling minutes "m", we can rewrite the above equation like this:
Cost company A = 0.05m + 20
Similarly for company B, we can write the following equation:
Cost company B = 0.1m + 5
By equating these equations, we can find how many minutes of calling would make the two plans equal, then we get:
Cost company A = Cost company B
0.05m + 20 = 0.1m + 5
From this expression, we can solve for m to get:
0.05m + 20 = 0.1m + 5
20 - 5 = 0.1m - 0.05m
15 = 0.05m
15/0.05 = m
300 = m
m = 300
Then, 300 minutes of calling would make the two plans equal
By replacing 200 for m into both models, we get:
Cost company A = 0.05(200) + 20 = 30
Cost company B = 0.1(200) + 5 = 25
As ou can see company B charges less than company A, then the plan that makes the most economic sense is company B