Integrated Math Name ________________ Date _________ Period ___
Solving word problems using inequalities
Write an inequality that represents each situation.
Solve inequality and write an answer as a sentence.
1. Jim is recording songs onto a CD. Each song is 50 MB. He already recorded
220 MB of the 700 MB CD. How many more songs can he record onto the
CD?
2. Bill is also recording songs onto a CD. He has already recorded 4 songs of 40
MB. If the CD can hold 650 MB, how many more 40 MB songs can Bill
record?
3. A student scored 71, 83, and 96 on three algebra tests. What must he score
on the fourth test in order to have an average grade of at least 85?
4. You rent a car and are offered 2 payment options. You can pay $25 a day
plus 15¢ a mile (option A) or you can pay $10 a day plus 40¢ a mile (option B).
For what amount of daily miles will option A be the cheaper plan?
5. To get a grade of C in your course, you must average at least 75 on 4 exams.
You have taken the first three exams and gotten scores of 68, 78, and 81.
What must you score on the last exam to get a C or better?
6. You have just been given a new job in sales. You have two salary options.
You can receive a straight salary of $500 per week (no commission option) or
you can receive a salary of $200 per week plus 5% of your weekly sales
(commission option). What dollar amount of product must you sell each week
in order for the commission option to be the better deal?
7. Abigail drove h hours at rate of 55 mi/h. She did not reach her goal of
driving 385 miles for the day. How long did she drive?
8. Anne buys a plant whose height is 6 cm. The plant is growing at a rate of
2/3 cm per week. When will its height exceed 10 2/3 cm?
9. Ian wants to promote his band on the internet. Site A offers website
hosting for $4.95 per month with a $49.95 startup fee. Site B offers
website hosting for $9.95 per month with no startup fee. For how many
months would Ian need to keep the website for site B to be less expensive
than site A.
10. You need 30 tons of rock to cover your backyard area. If each ton cost $60
and each tree is $84, what is the maximum number of trees you can by with
a budjet for rock and trees of $2,500?
11. Write an absolute value equation that represents all points exactly 2 units
from 3?
12. A box must be within 0.1 inch of 20 inches. Write an absolute value
inequality that represents all possible lengths of the box.
13. A box must be within 1 foot of 9 feet. Write an absolute value inequality
that represents all possible lengths of a box.
14. Write an absolute value inequality that represents all points within 5 units
from 6.
15. Write an absolute value inequality that represents all points within 10 units
from 4.
16. The hourly wages at a local business are between $8.60 and $14.80
depending upon the job. Write an absolute value inequality describing the
possible hourly wages of the employees.
17. The attendance at home basketball games has ranged between 820 and
spectators. Write an absolute value inequality describing the possible
attendance at home basketball games.
18. The post office will charge for the packages, which weigh at least 1 pound
and not exceeding 3 pound the same amount. Write an absolute value
inequality describing the possible weight of the packages.
19. A box is 25 inches long, 12 inches wide and 8 inches high when the
dimensions are rounded to the nearest inch. Assuming the margin of error is
± 5. Write and solve an absolute value inequality that describes the volume V
of the box.
20. A manufacturer has a 0.6oz tolerance for a bottle of salad dressing
advertized as 16oz. Write and solve an absolute value inequality that
describes the acceptable volumes for “16oz” bottles.
21. A city ordinance states that pools must be enclosed by a fence that is from
3 to 6 feet high. Write an absolute value inequality describing fences that
don’t meet this ordinance.