Question

Moving company a charge is $20 per man - hour plus a fixed base charge of $500. Moving company be charges $25 per man – hour with a fixed base charge of $300. Write equations to model each companies charge. Under what conditions (number of men – hours) would you choose to pay the higher base charge (company a)?

Answer 1

We can formulate the equations to model each company by adding the fixed charge to the charge due to man - hour contribution, like this:

Total charge = man-hour charge + fixed charge

For company a, the fixed charge is $500, then we can rewrite the above equation to get:

a = man-hour charge + 500

Where a is the total charge for the company a. The man-hour charge can be calculated by multiplying the man-hour number by the charge per man-hour, like this:

a = 20x + 500

Similarly, for company b:

b = 25x + 300

By equating these expressions we can find the value at which the total charge of both is the same

25x + 300 = 20x + 500

25x - 20x + 300 = 20x - 20x + 500

5x + 300 = 500

5x + 300 - 300 = 500 - 300

5x = 200

5x/5 = 200/5

x = 40

Then, for a man-hour number greater than 40 it is better to pay the company a charge