Final answer:
To find the cost for each company, write a system of equations and determine when the costs are equal. If it takes at least 35 hours to complete the job, Flourish Landscaping Company will be less expensive.
Step-by-step explanation:
To write a system of equations representing how much each company charges, we can let x represent the number of hours worked. For Flourish Landscaping Company, the cost is a flat rate of $120 per hour, so the equation would be:
Cost for Flourish = $120x
For Green Thumb Landscapers, the cost is $70 per hour plus a $1600 equipment fee, so the equation would be:
Cost for Green Thumb = $70x + $1600
To determine the number of hours that must be worked for the cost of each company to be the same, we can set the two equations equal to each other and solve for x:
$120x = $70x + $1600
$50x = $1600
x = 32
So 32 hours must be worked for the cost of each company to be the same.
If it is estimated to take at least 35 hours to complete the job, we can substitute x = 35 into the equations to find the cost for each company:
Cost for Flourish = $120 * 35 = $4200
Cost for Green Thumb = $70 * 35 + $1600 = $3850 + $1600 = $5450
Therefore, the company that will be less expensive is Flourish Landscaping Company.