Question

IVan charges an hourly rate for a moving team to load and unload a truck. The charge is a different

hourly rate for a team to pack and unpack boxes. For 8 hours of loading and unloading and 6 hours of


packing and unpacking the company charges $890. For 5 hours of loading and unloading and 3 hours of


packing and unpacking the company charges $515. Write a system of equations and then determine the


company's hourly rates?

Answer 1

The hourly rates for loading and unloading and packing and unpacking are $70 and $55, respectively.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations based on the given information. Let's denote the hourly rate for loading and unloading as 'L' and the hourly rate for packing and unpacking as 'P'.

From the first scenario, we know that 8L + 6P = 890.

From the second scenario, we know that 5L + 3P = 515.

Using these equations, we can solve for the values of 'L' and 'P' to find the company's hourly rates.

Multiplying the second equation by 2, we get 10L + 6P = 1030.

Subtracting the revised second equation from the first equation, we have 8L + 6P - (10L + 6P) = 890 - 1030.

Simplifying, we get -2L = -140. Dividing both sides by -2, we find that L = 70.

Substituting this value back into the second equation, we can solve for P: 5(70) + 3P = 515.

Simplifying, we get 350 + 3P = 515. Subtracting 350 from both sides, we have 3P = 165.

Dividing both sides by 3, we find that P = 55.

Therefore, the company's hourly rates are $70 for loading and unloading and $55 for packing and unpacking.

Answer 2

To determine the company's hourly rates, we can set up a system of equations using the given information and solve for the variables. The company's hourly rates are $75 for loading and unloading and $50 for packing and unpacking.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations using the given information. Let's denote the hourly rate for loading and unloading as 'x' and the hourly rate for packing and unpacking as 'y'.

From the first set of information, we can write the equation: 8x + 6y = 890. From the second set of information, we can write the equation: 5x + 3y = 515.

To solve this system of equations, we can use the method of substitution or elimination. By solving the system, we find that the company's hourly rates are x = $75 and y = $50.