Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Two car owners are in need of car repairs. Harold will need to pay the mechanic $4 per minute for labor, plus $366 to cover the cost of new parts. Doug will need to pay $392 for parts and $2 per minute for labor. Depending on how long each repair takes, the two jobs might end up costing the same amount. How much time would that take? How much would Harold and Doug each have to pay? If the repairs took _____ minutes, Harold and Doug would each pay $_____.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Two car owners are in need of car repairs. Harold will need to pay the mechanic $4 per minute for labor, plus $366 to cover the cost of new parts. Doug will need to pay $392 for parts and $2 per minute for labor. Depending on how long each repair takes, the two jobs might end up costing the same amount. How much time would that take? How much would Harold and Doug each have to pay?   If the repairs took _____ minutes, Harold and Doug would each pay $_____.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables. Let x represent the number of minutes the labor takes. Let y represent the total cost for the repairs.Harold's Total Cost: Write the equation for Harold's total cost. Harold's cost for labor is $4 per minute, and he has a parts cost of $366. The equation for Harold's total cost is y = 4x + 366.Doug's Total Cost: Write the equation for Doug's total cost. Doug's cost for labor is $2 per minute, and he has a parts cost of $392. The equation for Doug's total cost is y = 2x + 392.Set Equations Equal: Set the two equations equal to each other to find the value of x when the costs are the same. 4x + 366 = 2x + 392Solve for x: Solve for x by subtracting 2x from both sides of the equation. 4x - 2x + 366 = 2x - 2x + 392 2x + 366 = 392Isolate Variable x: Subtract 366 from both sides to isolate the variable x. 2x + 366 - 366 = 392 - 366 2x = 26Divide to Solve x: Divide both sides by 2 to solve for x. 2x / 2 = 26 / 2 x = 13Find Total Cost: Use the value of x to find the total cost y for both Harold and Doug. We can use either equation, but let's use Harold's equation: y = 4x + 366. y = 4(13) + 366 y = 52 + 366 y = 418Check Solution: Check the solution by plugging x into Doug's equation to ensure it gives the same y value. y = 2x + 392 y = 2(13) + 392 y = 26 + 392 y = 418

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