Solve multi-step inequalities, including reversing the inequality when appropriate.
Match a context to the right multi-step inequality
Problem
A bus costs \(\$10\) plus \(\$3~\text{per}~\text{rider}\), with a total of at most \(\$40\). Let \(r\) be a nonnegative whole number. Which complete response correctly handles the situation?
A. \(10~+~3r~\le~40\) B. \(10~+~3r~\ge~40\) C. \(10~+~3r~<~40\)
Big Picture
What this problem is really about
Match the cost structure first: ten dollars is fixed, three dollars repeats per rider, and “at most forty” includes the limit while pointing toward smaller totals. Solve that model with equality-preserving operations. Because r counts riders, finish by keeping only nonnegative whole numbers and report the entire permitted set rather than treating the upper boundary as the only result.
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