a moving company charges $840 plus $17 per hour. Another moving company charges $760 plus $22 per hour. How long is a job that costs the same no matter which company is used?
Accepted Solution
A:
Equation: 840+17x=760+22x Solve for x x=16 see proof. 17 x + 840 = 22 x + 760 Subtract 22 x from both sides: (17 x - 22 x) + 840 = (22 x - 22 x) + 760 17 x - 22 x = -5 x: -5 x + 840 = (22 x - 22 x) + 760 22 x - 22 x = 0: 840 - 5 x = 760 Subtract 840 from both sides: (840 - 840) - 5 x = 760 - 840 840 - 840 = 0: -5 x = 760 - 840 760 - 840 = -80: -5 x = -80 Divide both sides of -5 x = -80 by -5: (-5 x)/(-5) = (-80)/(-5) (-5)/(-5) = 1: x = (-80)/(-5) The gcd of -80 and -5 is -5, so (-80)/(-5) = (-5×16)/(-5×1) = (-5)/(-5)×16 = 16: Answer: x = 16