Writing Equations Using Symbols

Lesson 1 Summary
Begin all word problems by defining your variables. State clearly what you want each symbol to represent.
Written mathematical statements can be represented as more than one correct symbolic statement.
Break complicated problems into smaller parts or try working them with simpler numbers.

Classwork
Discussion
Compare the mathematical statement to the equation.
Example 1
Express the following statement using symbolic language:
1 a)A whole number has the property that when half the number is added to fifteen, we get back the number itself.
1 b)A whole number has the property that when the square of half the number is subtracted from five times the number, we get back the number itself.

Example 2
Express the following statement using symbolic language:
Paulo has a certain amount of money. If he spends six dollars, then he has 1/4 of the original amount left.

Example 3
Write the following statement using symbolic language:
When a fraction of 57 is taken away from 57, what remains exceeds 2/3 of 57 by 4.

Example 4
Express the following statement using symbolic language:
The sum of three consecutive integers is 372.

Example 5
Express the following statement using symbolic language:
The sum of three consecutive odd integers is 93.

Exercises 1–5
Write each of the following statements using symbolic language.
1. The sum of four consecutive even integers is -28.
2. A number is four times larger than the square of half the number.
3. Steven has some money. If he spends nine dollars, then he will have 3/5 of the amount he started with.
4. The sum of a number squared and three less than twice the number is 129.
5. Miriam read a book with an unknown number of pages. The first week she read five less than 1/3 of the pages. The second week she read 171 pages and finished the book. Write an equation that represents the total number of pages in the book.