Final answer:
To determine the break-even point, calculate when the total cost equals the total revenue. The equation for break-even is obtained by setting 9x+1500 equal to 34x. Solving for x gives the result of 60 rides needed to break even.
Step-by-step explanation:
The student's question asks for the number of rides needed to break even when the cost for fuel and maintenance of a go-cart is given by c=9x+1500, where x is the number of rides, and it costs $34 per ride. To find the break-even point, we set the total cost equal to the total revenue. The total revenue from x rides is 34x (since each ride costs $34).
To find the break-even point, solve for x when total costs are equal to total revenue:
9x + 1500 = 34x
Subtract 9x from both sides:
1500 = 25x
Divide both sides by 25:
x = 60
Therefore, it requires 60 rides to break even.