Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Write and solve a linear inequality from a fixed amount and a constant rate
Problem
An amusement park charges a fixed \(\$8\) entry fee plus \(\$6~\text{per}~\text{ride}\), and a rider can spend at most \(\$50\). Let \(r\) be the number of rides. Write and solve a linear inequality for \(r\), then report the real solution and \(\text{all}~\text{valid}~\text{whole}\text{-}\text{number}~\text{ride}~\text{counts}\).
Big Picture
What this problem is really about
The spending cap turns the fixed-fee model into an inequality instead of an equation. We’ll translate “at most” with an inclusive comparison, subtract the entry fee, divide by the positive per-ride rate, and then restrict the real solution to nonnegative whole numbers because rides are counted.
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