Question

I have a word problem I'm unsure how to solve.

two plumbers make house calls. one charges $120 for a visit plus $45 per hour of work. The other charges $90 per visit plus $55/hr. For how many hours of work do the two plumbers charge the same?

I'm not really sure where to start, i've come up with 45x+120=c and 55x+90=c, I'm not sure if that's where i need to be thinking or how to solve??

Answer 1

okay, those are both valid, if c is the amount of the charge, and x is the hours worked. You want to find the value of x where the two equations give the same value for c, so just set 45x + 120 = 55x + 90 and solve for x.

Answer 2

I've never seen an equation like this so do I just solve like i normally would and just get the x to one side? Does it matter which side I get x on?

Answer 3

Exactly, and no. Because the two sides are equal, you can just flip them around, right? 2=2, and 2=2 — no difference, right?

Answer 4

Ok great.... so is the correct answer 3?

Answer 5

Another way you could solve this problem would be to draw a little graph. One plumber's price starts out a bit higher, but has a shallower slope. The other starts lower, but has a steeper slope. The point where the two lines intersect is the spot where the x value is the number of hours where they have the same charge.

Answer 6

and it looks like the lines cross at x = 3, doesn't it?

let's check with the formulas:

45(3)+120 = 55(3)+90
135+120 = 165+90
255 = 255
looks like x = 3 is the correct answer, good job!