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Lucie is struggling with Geometry and is in need of a private tutor. She has two candidates in mind. The veteran tutor charges $15 for the first session plus $60 per hour afterward. The new college graduate charges $45 for the first session plus $50 per hour afterward. How many hours must these two tutor in order to earn the same amount of money?

Respuesta :

MrRoyal

Answer:

2.33 hours

Step-by-step explanation:

Given

Veteran Tutor

[tex]Charges = \$15[/tex] --- first session

[tex]Hourly\ Rate = \$60[/tex]

College Graduate

[tex]Charges = \$45[/tex] --- first session

[tex]Hourly\ Rate = \$50[/tex]

Required

Determine the number of hours they earn the same amount

Represent the hours with x

First, we need to calculate the total charges for the veteran tutor for x hours;

[tex]Total = 15 + 60x[/tex]

Next, we need to calculate the total charges for the college graduate tutor for x hours;

[tex]Total = 45x + 50[/tex]

For them to earn the same amount, we have:

[tex]15 + 60x = 45x + 50[/tex]

Solving for x

[tex]60x - 45x = 50 - 15[/tex]

[tex]15x = 35[/tex]

Divide through by 15

[tex]x = \frac{35}{15}[/tex]

[tex]x = 2.33\ hours[/tex]

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