A1 Plumbing Service charges $35 per hour plus a $25 travel charge for a service call. Good Guys Plumbing Repair charges $40 per hour for a service call with no travel charge. How long must a service call be for the two companies to charge the same amount?

solving 35x+25=40x i.e x=5hrs

The trick with this kind of question is converting the text into mathematical notation. Once you've done that, it's usually pretty simple to get the answer.   In this case, we're interested in the total amount charged by each plumber and we want to know how that varies depending on the length of the call. That means we're going to want two formulae for the total cost depending on the length of the call.   The first formula, for A1, is:   Cost = $35 * time (in hours) + $25 (you may want to write that as C=35t+25 for simplicity)   The second is: Cost = $40 * time (in hours) (C=40t)   Now we have those formulae, it should be easy. The question is what length of time gives the same total cost, so we just equate the two formulae:   35t+25=40t   We now solve that equation in the usual way, by collecting all the terms with t in them on one side. We can do that by subtracting 35t from each side to get:   25=5t   We then divide by 5 and get t=5.   We're not quite done, though. We need to convert that back into the terms of the question. t was our abbreviation for time in hours, so our final answer is:   The cost of the two plumbers will be the same if the call lasts 5 hours.   (Don't forget that last bit - just saying "t=5" doesn't answer the question that was actually asked.)

The equation expressing A1 Plumbing Service’s charge for a service call is: Ca = 35h + 25, where h is the number of hours used for a service call.   The equation expressing Good Guys Plumbing Repair’s charge for a service call is:   Cg = 40h   To find how long a service call must be in order for the two companies to charge the same amount, we’ll set their respective charges equal to each other and then solve for h as follows:   Ca = Cg   35h + 25 = 40h   40h = 35h + 25 since equality is symmetrical, i.e., if a = b, then b = a for                           any real numbers a and b.   40h ‒ 35h = 35h ‒ 35h + 25   (40‒ 35)h = 0 + 25   5h = 25   (5h)/5 = 25/5   (5/5)h = 25/5   (1)h = 5   h = 5 hours is how long a service call must be in order for the two companies to charge the same amount.   Check (very important): Ca = Cg 35h + 25 = 40h 35(5) + 25 = 40(5) 175 + 25 = 200 200 = 200