EXAMPLE 1 Translate verbal phrases into expressions Verbal

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

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

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

EXAMPLE 3 Use a verbal model to write an expression Tips 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. SOLUTION STEP 1 Write a verbal model. STEP 2 Translate the verbal model into an algebraic expression. Let a represent the amount (in dollars) in the jar. Amount in jar Number of people a 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

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

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 afterwork celebration. Write an expression that represents the total amount (in dollars) contributed. ANSWER 6 d, where d represents the amount contributed by each worker.

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

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. SOLUTION STEP 1 Calculate the unit rate. 3. 75 0. 25 = = $. 25 per minute 15 1

EXAMPLE 5 Solve a multi-step problem STEP 2 Write a verbal model and then an expression. Let m be the number of extra minutes. 30 + 0. 25 m Use unit analysis to check that the expression 30 + 0. 25 m is reasonable. dollars + minutes = dollars + dollars = dollars minute Because the units are dollars, the expression is reasonable.

EXAMPLE 5 Solve a multi-step problem STEP 3 Evaluate the expression when m = 22. 30 + 0. 25(22) = 35. 5 ANSWER The total bill is $35. 50.