Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Write a system of inequalities for multiple constraints
Problem
Notebooks cost \(\$3\) each and pens cost \(\$2\) each. You may spend at most \(\$30\) and buy at most \(12\) items. Let \(x\) and \(y\) be the nonnegative whole-number counts of notebooks and pens. Write a system representing all constraints.
Big Picture
What this problem is really about
There are two independent limits here, so one inequality cannot capture the whole situation. We’ll build a dollar expression by pairing each price with its item count, write a separate inequality for the total number of items, and include the nonnegative whole-number conditions. A purchase is feasible only when all of those requirements hold at the same time.
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