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EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the...
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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
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Transcript of EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the...
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 – m2
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 + x2
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.
EXAMPLE 2 Write an expression
ANSWER
The expression 8 – l represents the length (in feet) of the remaining piece.
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 2Amount
in jarNumber
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
lp
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.
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 miles2 hours 2
110 miles 2 =
The unit rate is 55 miles per hour, or 55 mi/h.
ANSWER
SOLUTION
EXAMPLE 5 Solve a multi-step problem
Cell PhonesYour 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.
153.75
= 0.25 1 = $.25 per minute
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.
minutedollarsdollars + minutes = dollars + dollars = dollars
Because the units are dollars, the expression is reasonable.
STEP 2
30 + 0.25 m
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
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
