Application: Play Tickets

Property To solve word problems, first define your variables (e.g., let $x$ be adults and $y$ be students). Then, translate the words into two linear equations. Look for totals and relationships to build your system, such as $x + y = \text{total people}$ and $ax + by = \text{total dollars}$. Explanation Word problems are just puzzles in disguise! Your mission is to find the two hidden equations. First, identify what you don't know and assign variables like $x$ and $y$. Then, read carefully to find two facts or totals that connect them. One equation often deals with the quantity of items, and the other deals with their value. Examples Apples cost 2 dollars and bananas cost 1 dollar. You buy 10 fruits for 14 dollars. Let $a$ be apples, $b$ be bananas. The equations are $a+b=10$ and $2a+b=14$. From $a+b=10$, we get $b=10 a$. Substitute into the second equation: $2a + (10 a) = 14$, so $a+10=14$, which means $a=4$. If you have 4 apples, use $a+b=10$ to find bananas: $4+b=10$, so $b=6$. You bought 4 apples and 6 bananas.