Final answer:
To determine how many hours of tutoring would cost the same between a base rate of $20 plus $8 per hour and a set rate of $13 per hour, set up an equation $20 + $8x = $13x and solve for x. If the student needs 4 hours of tutoring, both options would cost the same.
Step-by-step explanation:
To determine how many hours of tutoring would cost the same between a base rate of $20 plus $8 per hour and a set rate of $13 per hour, we can set up an equation. Let x be the number of hours of tutoring. For the first option, the cost would be $20 + $8x. For the second option, the cost would be $13x. We can now set these two expressions equal to each other and solve for x:
$20 + $8x = $13x
Subtracting $8x from both sides, we get:
$20 = $5x
Dividing both sides by $5, we find that x = 4. So, if the student needs 4 hours of tutoring, both options would cost the same.