Solve linear equations and inequalities in one variable, including literal linear equations.
Solve and interpret a context inequality
Problem
A \(\$50\) budget buys tickets at \(\$8\) each. Let \(t\) be a nonnegative whole-number count. Write and solve the inequality, then give the greatest allowed whole number of tickets.
Big Picture
What this problem is really about
The budget limits a total cost, while the variable counts objects rather than arbitrary real numbers. We’ll multiply the per-ticket price by the count, translate the upper-limit language into an inequality, and solve the real-valued bound with attention to the coefficient’s sign. Then we’ll restrict that bound to nonnegative whole numbers and check the greatest feasible count against the next integer.
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