Problem

Analyze \(C(n)=3n+12\) when \(n\) counts items and \(C\) is dollars. Assign units to \(3\) and \(12\), determine the units of \(3n\), and justify why the two terms can be added.

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n has units of items; 3 has units of dollars per item; 12 has units of dollars. The product 3n has dollars, and dollars + dollars gives C in dollars.

n has units of items; 3 is a unitless multiplier; 12 has units of dollars. The product 3n has items, so C has items plus dollars.

n has units of items; 3 has units of dollars per item; 12 has units of dollars. The operation adds 3 + n, so C has dollars per item plus items.

n has units of items; 3 has units of dollars per item; 12 has units of dollars. Because dollars and items are different units, 3n and 12 cannot be added, so C has no units.

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Analyze \(C(n)=3n+12\) when \(n\) counts items and \(C\) is dollars. Assign units to \(3\) and \(12\), determine the units of \(3n\), and justify why the two terms can be added.

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