Emma wants to hire a photographer to take graduation photos for her and her friends. She found a local photographer who charges $120 per hour. She also found an out-of-town photography student who charges $75 per hour, plus a $90 travel fee.

Question

How long would the photo session need to last for the total cost for either photographer to be the same?

Answer 1

To determine the point at which the total cost for both photographers is the same, we can set up equations based on the information given:

1. The local photographer charges $120 per hour. Therefore, the cost for \( x \) hours is: \[ C_1 = 120x \]

2. The out-of-town photography student charges $75 per hour plus a $90 travel fee. Thus, the total cost for \( x \) hours is: \[ C_2 = 75x + 90 \]

Now, we set the costs equal to each other to find the value of \( x \) where they are the same: \[ 120x = 75x + 90 \]

Next, we will solve for \( x \):

1. Subtract \( 75x \) from both sides: \[ 120x - 75x = 90 \] \[ 45x = 90 \]

2. Now, divide both sides by 45: \[ x = \frac{90}{45} = 2 \]

Therefore, the photo session would need to last for 2 hours for the total cost for either photographer to be the same.