Define each unknown with its unit, then translate two independent pieces of information into two equations. After solving, check both the arithmetic and the context, including whether a count must be a nonnegative integer. Example At an event, adult tickets cost 12 dollars and child tickets cost 7 dollars. A group buys 8 tickets for 76 dollars. Let a and c be the adult and child ticket counts. a+c=8 and 12a+7c=76. Subtracting 7a+7c=56 from the cost equation gives 5a=20, so a=4 and c=4. Check: 4+4=8 tickets and 4(12)+4(7)=76 dollars. The solution gives counts, not ticket prices.

Define each unknown with its unit, then translate two independent pieces of information into two equations. After solving, check both the arithmetic and the context, including whether a count must be a nonnegative integer.

At an event, adult tickets cost \(12\) dollars and child tickets cost \(7\) dollars. A group buys \(8\) tickets for \(76\) dollars. Let \(a\) and \(c\) be the adult and child ticket counts.

\(a+c=8\) and \(12a+7c=76\). Subtracting \(7a+7c=56\) from the cost equation gives \(5a=20\), so \(a=4\) and \(c=4\).

Check: \(4+4=8\) tickets and \(4(12)+4(7)=76\) dollars. The solution gives counts, not ticket prices.

Forming a two-variable model

Forming a two-variable model