Question

Sheila is planning to move from New York to Arizona. She obtained a price quote from two moving companies. Company A charges a one-time processing fee of $230 and $3.40 for every pound moved. Company B charges a one-time processing fee of $270 and $2.80 for every pound moved.

Part A. Write an expression that represents the rate each company charges. Let x represent the number of pounds to be moved.
Part B. If Sheila has a total of 1250 pounds of household items, which company would charge less to move her items? Show your work and explain how you got your answer.

Answer 1

To write an expression that represents the rate each company charges, use the formula: Rate = (one-time processing fee) + (price per pound * number of pounds). For Company A, the rate is $230 + $3.40 * x pounds. For Company B, the rate is $270 + $2.80 * x pounds. To determine which company would charge less to move 1250 pounds of household items, calculate the total cost for each company. Based on the calculations, Company B would charge less.

Step-by-step explanation:

Part A:

To write an expression that represents the rate each company charges, we can use the formula:

Rate = (one-time processing fee) + (price per pound * number of pounds)

For Company A, the rate is:

RateA = $230 + $3.40 * x

For Company B, the rate is:

RateB = $270 + $2.80 * x

Part B:

To determine which company would charge less to move 1250 pounds of household items, we can compare the total cost for each company.

For Company A, the total cost is:

Total CostA = $230 + $3.40 * 1250

For Company B, the total cost is:

Total CostB = $270 + $2.80 * 1250

We can calculate the total costs for both companies to find out which one charges less.

Calculations:

Total CostA = $230 + $3.40 * 1250 = $230 + $4250.00 = $4480.00

Total CostB = $270 + $2.80 * 1250 = $270 + $3500.00 = $3770.00

Therefore, Company B would charge less to move Sheila's items.