Question 145937: 3. You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.
a) Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?
b) Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?
c) For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.
Answer by BrittanyM(80)   (Show Source):
You can put this solution on YOUR website! First, let's set up equations to represent the charges of the two different moving companies.
For Heavy Lifters, the initial fee is 80 plus an additional 35 for each hour.
H(x) = 35x + 80
Quick Move has no initial fee, and charges 55 per hour.
Q(x) = 55x
In "a", we are asked to find the best company for two hours of work.
H(2) = 35(2) + 80
H(2) = 150
Q(2) = 55(2)
Q(2) = 110
So by comparision, we know that Quick Movers is a better deal for two hours of work.
In "b", we are asked to find the best movers for fifteen hours of work.
H(15) = 35(15) + 80
H(15) = 605
Q(15) = 55(15)
Q(15) = 825
For fifteen hours, Heavy Movers is the best choice.
Lastly, for "c", we are asked to find the time at which Quick Movers is the better deal.
We first find the time at which both companies charge the same amount.
55x = 35x + 80
x = 4
By using test numbers, one greater than four, and one less than four, we can determine which values each compny offers the best deals.
H(5) = 255
Q(5) = 275
H(3) = 185
Q(3) = 165
With this, we see that anything less than or equal to 4 hours makes Quick Move a greater deal.
Quick Movers is the better deal where h =< 4
|
|
|
