The document provides examples and guidance for writing algebraic expressions and solving applied problems and puzzles involving variables. It shows how to set up equations using variables to represent unknown quantities, write expressions in terms of those variables, and then solve the equations. The examples demonstrate representing word problems algebraically and include problems about amounts of homework, numbers of games won and lost, ages, attendance at events, and finding consecutive numbers. Students are assigned related practice problems at the end.
2. Example
Laura has twice as much homework as Ann.
Let x be Ann’s amount of homework.
Then __?__ is Laura’s amount.
3. Example
Chicago lost 5 more games than it won.
Let x = the number of games won.
Then __?__ = number of games lost.
4. Example
George is y years old today.
His age in 5 years will be __?__ .
His age last year was __?__ .
5. Example
Caroline is 3 years older than Sam.
Let c = Caroline’s age.
Then __?__ is Sam’s age.
In 3 years, Caroline’s age will be __?__ .
In 3 years, Sam’s age will be __?__ .
6. A Guide for Problem Solving
1. Read the problem.
2. Let a variable stand for one of the unknowns.
Show the other unknowns in terms of that
variable.
3. Write an equation and solve it.
4. Answer the question.
5. Check your answer.
7. Example
Ed has twice as much money as Jake.
Together they have $54.
How much money does each have?
8. Example
A basketball team played 25 games.
They won 7 more games than they lost.
How many games did they win and lose?
9. Example
The school play ran for two nights.
A total of 200 people attended.
There were 50 more people on the second night.
How many people attended both nights?
