Question

a consultant charges $45 for each hour she works on a consultation, plus flat $30 consulting fee. how many hours of work are included in a $210 bill for a consultation?

Explanation:

Step1: Define the cost function

Let \( h \) be the number of hours. The total cost \( C \) is the flat fee plus the hourly rate times hours, so \( C = 30 + 45h \).

Step2: Set up the equation

We know the total bill \( C = 210 \), so substitute into the equation: \( 210 = 30 + 45h \).

Step3: Solve for \( h \)

Subtract 30 from both sides: \( 210 - 30 = 45h \), which simplifies to \( 180 = 45h \). Then divide both sides by 45: \( h=\frac{180}{45}=4 \).

Answer:

4