1. EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the quantity 6 times a number n b. 3 times the sum of 7 and a number y c. The difference of 22 and the square of a number m 6n – 4 3(7 + y) 22 – m 2

2. GUIDED PRACTICE for Example 1 1. Translate the phrase “the quotient when the quantity 10 plus a number x is divided by 2 ” into an expression. ANSWER 1. Expression 10 + x 2

3. SOLUTION Cutting A Ribbon EXAMPLE 2 Write an expression A piece of ribbon l feet long is cut from a ribbon 8 feet long. Write an expression for the length (in feet) of the remaining piece. Draw a diagram and use a specific case to help you write the expression. Suppose the piece cut is 2 feet long. Suppose the piece cut is L feet long. The remaining piece is ( 8 – 2 ) feet long. The remaining piece is ( 8 – l ) feet long.

4. EXAMPLE 2 Write an expression ANSWER The expression 8 – l represents the length (in feet) of the remaining piece.

5. Write a verbal model. SOLUTION You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount in the jar equally at the end of the day. Write an expression for each person’s share (in dollars) of the tips. Tips EXAMPLE 3 Use a verbal model to write an expression Translate the verbal model into an algebraic expression. Let a represent the amount (in dollars) in the jar. STEP 1 STEP 2 Amount in jar Number of people  a  6

6. EXAMPLE 3 Use a verbal model to write an expression ANSWER An expression that represents each person’s share (in dollars) is. a 6

7. GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 2, suppose that you cut the original ribbon into p pieces of equal length. Write an expression that represents the length (in feet) of each piece. ANSWER l p

8. GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 3, suppose that each of the 6 workers contributes an equal amount for an after- work celebration. Write an expression that represents the total amount (in dollars) contributed. ANSWER 6d, where d represents the amount contributed by each worker.

9. EXAMPLE 4 Find a unit rate A car travels 110 miles in 2 hours. Find the unit rate. 110 miles 2 hours = 1 hour 55 miles 2 hours 2 110 miles 2 = The unit rate is 55 miles per hour, or 55 mi/h. ANSWER

10. SOLUTION EXAMPLE 5 Solve a multi-step problem Cell Phones Your basic monthly charge for cell phone service is $30, which includes 300 free minutes. You pay a fee for each extra minute you use. One month you paid $3.75 for 15 extra minutes. Find your total bill if you use 22 extra minutes. STEP 1 Calculate the unit rate. 15 3.75 = 0.25 1 = $.25 per minute

11. EXAMPLE 5 Solve a multi-step problem Write a verbal model and then an expression. Let m be the number of extra minutes. Use unit analysis to check that the expression 30 + 0.25m is reasonable. minute dollars dollars + minutes = dollars + dollars = dollars Because the units are dollars, the expression is reasonable. STEP 2 30 + 0.25 m

12. EXAMPLE 5 Solve a multi-step problem Evaluate the expression when m = 22. 30 + 0.25(22) = 35.5 ANSWER The total bill is $35.50. STEP 3

13. EXAMPLE 5 Solve a multi-step problem Evaluate the expression when m = 22. 30 + 0.25(22) = 35.5 ANSWER The total bill is $35.50. STEP 3