Inequalities

Section 10.3Solving Problems

Involving Inequalities

Example 1(see textbook)

Molly set her car’s trip odometer at zero at the start of her trip home. When the odometer showed that she had driven 16 miles, a highway sign showed her that she was still more than 25 miles from her home. What is the minimum total distance, to the nearest mile, that she will have traveled when she arrives home?

the distance in total miles

16 the distance from the sign to home

d

d

The distance from the sign to home is 25 milesmore t .

16 25

41

han

d

d

Translations

• At least • At most• No less than• No more than

Example 2 (text p. 470)Mike wants to rent a car for his vacation. The rental costs $125 a week plus $0.15 a mile. How far to the nearest mile can Mike travel if he wants to spend at most $200?

the number of miles Mike can travel

Cost of the car rent at mosal is .t $200

m

125 0.15 200

0.1

0

5 75

5 0

m

m

m

Example 3 (text p. 470)The width of a rectangular computer screen is 20 cm less

than twice the length. The perimeter is at least 53 cm. Find the minimum dimensions, in centimeters, of the screen if each dimension is an integer.

the length in centimeters

then 2 20 the width in centimeters

The perimeter is 53 centimeters.at least

l

l

2 2 2 20 53

2 4 40 53

6 93

15.5

l l

l l

l

l

The dimensions are 16 cm by 12 cm.

Assignment

• See syllabus