Linear Equations And Inequalities In One Variable Worksheet With Answer Key (Page 8 of 8) in pdf

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2.9 Solving Inequalities and Applications

a Coke is $0.25 more than the price of the fries. Burger

North

Brothers advertises that you can get a complete meal

(burger, fries, and Coke) for under $2.00. What is the price

range of an order of fries?

Lighthouse

Less than 44 cents

67. Averaging test scores. Tilak made 44 and 72 on the ﬁrst

two tests in algebra and has one test remaining. For Tilak to

pass the course, the average on the three tests must be at

least 60. For what range of scores on his last test will Tilak

pass the course?

F I G U R E F O R E X E R C I S E 7 3

At least 64

68. Averaging income. Helen earned $400 in January, $450 in

February, and $380 in March. To pay all of her bills, she must

average at least $430 per month. For what income in April

110

would her average for the four months be at least $430?

At least $490

69. Going for a C. Professor Williams gives only a midterm

exam and a ﬁnal exam. The semester average is computed

by taking

of the midterm exam score plus

of the ﬁnal

exam score. To get a C, Stacy must have a semester average

between 70 and 79 inclusive. If Stacy scored only 48 on the

midterm, then for what range of scores on the ﬁnal exam

F I G U R E F O R E X E R C I S E 7 4

will Stacy get a C?

Between 81 and 94.5 inclusive

75. Bicycle gear ratios. The gear ratio r for a bicycle is deﬁned

70. Different weights. Professor Williamson counts his

by the formula

midterm as

of the grade and his ﬁnal as

of the grade.

Wendy scored only 48 on the midterm. What range of

scores on the ﬁnal exam would put Wendy’s average be-

where N is the number of teeth on the chainring (by the

tween 70 and 79 inclusive? Compare to the previous

pedal), n is the number of teeth on the cog (by the wheel),

exercise.

and w is the wheel diameter in inches (Cycling, Burkett and

Between 114 and 141 inclusive

Darst).

71. Average driving speed. On Halley’s recent trip from Ban-

a) If the wheel has a diameter of 27 in. and there are 12

gor to San Diego, she drove for 8 hours each day and trav-

teeth on the cog, then for what number of teeth on the

eled between 396 and 453 miles each day. In what range

chainring is the gear ratio between 60 and 80?

was her average speed for each day of the trip?

Between 27 and 35 teeth inclusive

Between 49.5 and 56.625 miles per hour

b) If a bicycle has 48 teeth on the chainring and 17 teeth on

72. Driving time. On Halley’s trip back to Bangor, she drove

the cog, then for what diameter wheel is the gear ratio

at an average speed of 55 mph every day and traveled be-

between 65 and 70?

tween 330 and 495 miles per day. In what range was her

Between 23.02 in. and 24.79 in.

daily driving time?

c) If a bicycle has a 26-in. diameter wheel and 40 teeth on

Between 6 and 9 hours

the chainring, then for what number of teeth on the cog

73. Sailboat navigation. As the sloop sailed north along the

is the gear ratio less than 75?

coast, the captain sighted the lighthouse at points A and B as

At least 14 teeth

shown in the ﬁgure. If the degree measure of the angle at

76. Virtual demand. The weekly demand (the number bought

the lighthouse is less than 30°, then what are the possible

by consumers) for the Acme Virtual Pet is given by the for-

values for x?

mula

Between 55° and 85°

9000

60p

74. Flight plan. A pilot started at point A and ﬂew in the di-

where p is the price each in dollars.

rection shown in the diagram for some time. At point B she

a) What is the demand when the price is $30 each?

made a 110° turn to end up at point C, due east of where she

7200

started. If the measure of angle C is less than 85°, then what

b) In what price range will the demand be above 6000?

are the possible values for x?

Less than $50

Between 0° and 65°

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