Section 1.2 Introduction to Algebra and the Set of Real Numbers 21 356 124. Ayako took a trip to the store mi away. If she 120. A futon, when set up as a sofa, measures ft wide. 34 When it is opened to be used as a bed, the width is increased by 1ft.What is the total width of this bed? x in. 2638 456 512 ft 356 rode the bus for mi and walked the rest of the way, how far did she have to walk? 126. Pete started working out and found that he lost 34 approximately in. off his waistline every month. How much would he lose around his waist in 6 months? 614 3 4 112 116 234 38 26 Introduction to Algebra and the Set of Real Numbers Section 1.2 1. Variables and Expressions Doctors promote daily exercise as part of a healthy lifestyle. Aerobic exercise is exercise for the heart. During aerobic exercise, the goal is to maintain a heart rate level between 65% and 85% of an individual’s maximum recommended heart rate. The maximum recommended heart rate, in beats per minute, for an adult of age a is given by: Maximum recommended heart rate 220 a In this example, value a is called a variable.This is a symbol or letter, such as x, y, z, a, and the like, that is used to represent an unknown number that is subject to change. The number 220 is called a constant, because it does not vary. The quantity 220 a is called an algebraic expression. An algebraic expression is a collection of variables and constants under algebraic operations. For example, y 7, and t 1.4 are algebraic expressions. The symbols used in algebraic expressions to show the four basic operations are shown here: Addition Subtraction Multiplication a b a b, a b, 1a2b, a1b2, 1a21b2, ab (Note: We rarely use the notation because the symbol may be confused with the variable x.) Division a b, a b , ab, ba a b a b 3x , Concepts 1. Variables and Expressions 2. The Set of Real Numbers 3. Inequalities 4. Opposite of a Real Number 5. Absolute Value of a Real Number 119. A board in. long must be cut into three pieces of equal length. Find the length of each piece. 121. A plane trip from Orlando to Detroit takes hr. If the plane traveled for hr, how much time remains for the flight? 123. José’s catering company plans to prepare two different shrimp dishes for an upcoming event. One dish requires lb of shrimp and the other requires lb of shrimp. How much shrimp should José order for the two dishes? 125. If Tampa, Florida, averages in. of rain during each summer month, how much total rain would be expected in June, July,August, and September? 122. Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has lb of turkey in the cooler, and each sandwich requires lb of turkey. How many sandwiches can she make? 38 334
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