Stefan's family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an init
ial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee? If h represents the hourly fee, which equation models this problem? What was the hourly fee for the rototiller?
Let h represent the hourly fee for renting the rototiller.
The rental company charged an initial fee of $43 with an additional fee per hour. Assuming that they rented the rototiller for x hours. This means that if they rented the rototiller for x hours, the total amount that they would pay is
43 + hx
If they paid $64 after renting the rototiller for 7 hours, the equation that models this problem would be
First, subtract 43 from 64 to find how much the 7 hours on the rototiller actually costed them, which would be 21. Next, divide 21 by 7 to find the hourly fee, which would be 3. If h represented the hourly fee, the equation for this would be 64 = 7h + 43 meaning 64 (the total cost) is equal to 7 times the hourly fee (7 because she rented it for 7 hours) plus 43 (the initial fee).
Solve for x: 8 - 5 x = 2 x + 8 Subtract 2 x from both sides: 8 + (-5 x - 2 x) = (2 x - 2 x) + 8 -5 x - 2 x = -7 x: -7 x + 8 = (2 x - 2 x) + 8 2 x - 2 x = 0: 8 - 7 x = 8 Subtract 8 from both sides: (8 - 8) - 7 x = 8 - 8 8 - 8 = 0: -7 x = 8 - 8 8 - 8 = 0: -7 x = 0 Divide both sides of -7 x = 0 by -7: (-7 x)/(-7) = 0/(-7) (-7)/(-7) = 1: x = 0/(-7) 0/(-7) = 0: Answer: x = 0
