Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. The Harding family is looking to rent a large truck for their upcoming move. With Billy's Moving, they would pay $40 for the first day plus $7 per additional day. With Wildgrove Rent-a-Truck, in comparison, the family would pay $41 for the first day plus $6 per additional day. Before deciding on which company to use, Mrs. Harding wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be? How many additional days would that be? The Harding family would pay $_____ either way if they rented the truck for _____ additional days.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  The Harding family is looking to rent a large truck for their upcoming move. With Billy's Moving, they would pay $40 for the first day plus $7 per additional day. With Wildgrove Rent-a-Truck, in comparison, the family would pay $41 for the first day plus $6 per additional day. Before deciding on which company to use, Mrs. Harding wants to find out what number of additional days would make the two choices equivalent with regards to cost. What would the total cost be? How many additional days would that be?   The Harding family would pay $_____ either way if they rented the truck for _____ additional days.

Bytelearn · Accepted Answer

Set up equations: Set up the equations based on the given information. Billy's Moving cost: $40 for the first day + $7 per additional day. Wildgrove Rent-a-Truck cost: $41 for the first day + $6 per additional day. Let x represent the number of additional days, and C represent the total cost. Billy's Moving equation: C = 40 + 7x Wildgrove Rent-a-Truck equation: C = 41 + 6xSet equations equal: Since we want to find the number of additional days that would make the costs equivalent, we set the two equations equal to each other. 40 + 7x = 41 + 6xSolve for x: Solve for x by subtracting 6x from both sides of the equation. 40 + 7x - 6x = 41 + 6x - 6x 40 + x = 41Subtract to find x: Subtract 40 from both sides to solve for x. 40 + x - 40 = 41 - 40 x = 1Find total cost: Now that we have the number of additional days (x), we can find the total cost (C) by substituting x back into either of the original equations. We'll use Billy's Moving equation. C = 40 + 7x C = 40 + 7(1)Calculate total cost: Calculate the total cost. C = 40 + 7(1) C = 40 + 7 C = 47

Full solution

More problems from Solve a system of equations using any method: word problems

Related topics