Use commutative, associative, and distributive structure to rewrite and simplify numerical expressions efficiently.
Factor a common contextual rate or group count
Problem
A fundraiser sold \(18\) student tickets and \(32\) adult tickets at \(\$25~\text{each}\). Rewrite \(18\times~25~+~32\times~25\) by factoring out the common ticket price, then find the total.
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What this problem is really about
The two ticket groups share the same price per ticket. We’ll write their revenues as two products, factor the common ticket price, add the ticket counts inside parentheses, and then multiply once. This reverse-distributive rewrite counts every ticket at the shared rate.
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