You recently started the paper work for your new homeand you were just notified you can move in , in t0 weeks.You then decide to hire a moving company,but are unsure which company to choose.You search on line and are interestted in contacting 2 companies, Heavy lifters and Quick move,to discuss their rates.Heavy lifters charges an $80 fee + 35dollars an hour and Quiack move charges 55 dollars and no additional fees. For what values h (hours)does quick move offer a better deal? Express your answer as inequality. How did you rreach the answer?
To determine for what values of h (hours) Quick move offers a better deal, we need to compare the costs of both companies.
For Heavy lifters:
Cost = $80 (fixed fee) + $35 (per hour) * h (hours) = $80 + $35h
For Quick move:
Cost = $55 (per hour) * h (hours) = $55h
To find when Quick move offers a better deal, we need to set up an inequality to compare the costs. Since Quick move should offer a better deal, its cost should be less than the cost of Heavy lifters:
$55h < $80 + $35h
We can now solve this inequality:
$55h - $35h < $80
Simplifying the equation:
$20h < $80
Dividing both sides by 20:
h < $80 / $20
Simplifying further:
h < 4
Therefore, Quick move offers a better deal for values of h (hours) that are less than 4. In other words, if you plan to move within 4 hours, Quick move would be the more affordable option.
To reach this answer, I compared the cost functions of both companies by expressing them as mathematical equations. By setting up an inequality and solving it, we determined the range of hours where Quick move is more economical.