Basic Mathematics for College Students

Find the GCF of the given numbers.See Example 8.

Find the GCF of the given numbers.See Example 9.

Find the GCF of the given numbers.See Example 10.

TRY IT YOURSELF

Find the LCM and the GCF of the given numbers.

APPLICATIONS

85. OIL CHANGES Ford has officially extended the oil
    change interval for 2007 and newer cars to every
    7,500 miles. (It used to be every 5,000 miles).
    Complete the table below that shows Ford’s new
    recommended oil change mileages.

50, 81 65, 81

46, 69 38, 57

34, 68, 102 26, 39, 65

120, 125 98, 102

8, 9, 49 9, 16, 25

66, 198, 242 52, 78, 130

14, 140 15, 300

100, 120 120, 180

72, 108, 144 81, 108, 162

12, 68, 92 24, 36, 40

81, 125 57, 125

16, 51 27, 64

28, 42 63, 84

18, 96 30, 48

15, 30 15, 75

22, 33 14, 21

88. BIORHYTHMS Some scientists believe that there
    are natural rhythms of the body, called biorhythms,
    that affect our physical, emotional, and mental cycles.
    Our physical biorhythm cycle lasts 23 days, the
    emotional biorhythm cycle lasts 28 days, and our
    mental biorhythm cycle lasts 33 days. Each biorhythm
    cycle has a high, low and critical zone. If your three
    cycles are together one day, all at their lowest point,
    in how many more days will they be together again,
    all at their lowest point?


89. PICNICS A package of hot dogs usually contains
    10 hot dogs and a package of buns usually contains
    12 buns. How many packages of hot dogs and buns
    should a person buy to be sure that there are equal
    numbers of each?


90. WORKING COUPLES A husband works for
    6 straight days and then has a day off. His wife works
    for 7 straight days and then has a day off. If the
    husband and wife are both off from work on the
    same day, in how many days will they both be off
    from work again?


91. DANCE FLOORS A dance floor is to be made from
    rectangular pieces of plywood that are 6 feet by
    8 feet. What is the minimum number of pieces of
    plywood that are needed to make a square dance
    floor?

100 Chapter 1 Whole Numbers

1st oil 2nd oil 3rd oil 4th oil 5th oil 6th oil

change change change change change change

7,500 mi

Plywood

8 ft sheet

6 ft

Square

dance floor

12 ounces 21 ounces 18 ounces

86. ATMs An ATM machine offers the customer
    cash withdrawal choices in multiples of $20.
    The minimum withdrawal is $20 and the
    maximum is $200. List the dollar amounts
    of cash that can be withdrawn from the ATM
    machine.


87. NURSING A nurse is instructed to check a patient’s
    blood pressure every 45 minutes and another is
    instructed to take the same patient’s temperature
    every 60 minutes. If both nurses are in the patient’s
    room now, how long will it be until the nurses are
    together in the room once again?
    92. BOWLS OF SOUP Each of the bowls shown below
    holds an exact number of full ladlesof soup.
    a. If there is no spillage, what is the greatest-size
    ladle (in ounces) that a chef can use to fill all three
    bowls?
    b. How many ladles will it take to fill each
    bowl?