A landscaping company charges a one-time equipment mobilization fee of 45 plus an hourly l… — ACT

A landscaping company charges a one-time equipment mobilization fee of $45$ plus an hourly labor rate of $32.50$ per worker. A homeowner hires a crew of $3$ workers to clear their yard. If the total bill for the job is $435$ dollars, for how many hours did the crew work?

Answer: 4 hours

Answer

The total cost of

435

dollars is the sum of the one-time

45

dollar mobilization fee and the hourly labor cost of

32.50

dollars per worker for

3

workers over

h

hours. This translates to the equation

45 + 3(32.50)h = 435

, which simplifies to

45 + 97.50h = 435

. Subtracting

45

from both sides gives

97.50h = 390

. Dividing by

97.50

yields

h = 4

hours.

Step-by-Step Solution

Set up the algebraic expression representing the total cost based on the number of hours worked,

h

. The total cost consists of a fixed mobilization fee of

45

dollars and a variable labor cost of

32.50

dollars per worker per hour.

45 + 3(32.50)h

To represent the relation between the hours worked and the total charge.

Equate the expression for the total cost to the actual total bill of

435

dollars and simplify the labor rate coefficient.

45 + 97.50h = 435

To form a solvable linear equation in terms of the unknown number of hours,

h

Subtract the fixed mobilization fee of

45

from both sides of the equation.

97.50h = 390

To isolate the term containing the variable

h

Divide both sides of the equation by

97.50

to solve for

h

h = 4

To determine the number of hours the crew worked.

Key Concept

Formulating and solving linear equations from real-world contexts

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic