System of Inequalities Word Problems:
1. Sabrina works 40 hours or less per week as an aerobics instructor and tutor. She earns $10 per hour as an aerobics instructor and $20 per hour tutoring.
Sabrina needs to earn at least $500 per week. Write a system of linear inequalities that represents the possible number of hours spent at each job that will meet
Sabrina’s needs. Let x = number of hours spent as an aerobics instructor and y = number of hours spent tutoring.
a. Write a system of two inequalities that describes this situation.
40  x  y
or
y   x  40
$10 x  $20 y  $500
or
20 y  10 x  500
or
1
y   x  25
2
c. Name a point that is a solution of the system.
(30, 10) or (16, 20) or (10, 25)
2. Two typists are working on a statistical report. To finish on time, together, they need to type at least 30 pages per day. This is the first time typist A has typed
material that contains mostly numbers, so she may be expected to type no more than 2/3 as many pages as typist B. What are the acceptable combinations of
typing output that the typists might produce in a day?
a. Write a system of two inequalities that describes this situation.
A  B  30 or B   A  30
A
2
B
3
so B 
3
A
2
b. Graph the system to show all possible solutions.
c. Name a point that is a solution of the system.
(10, 40)
3. Some land on a farm, in the shape of a rectangle, is to be fenced as a feeder lot for cattle. The farmer wants the distance around the lot to be no more than
2600 ft. The length should be greater than 800 ft. What are the possible dimensions of the lot?
a. Write a system of two inequalities that describes this situation.
2l  2w  2600 or w  l  1300
l  800
b. Graph the system to show all possible solutions.
c. Name a point that is a solution of the system.
(1000, 200)
4. In basketball you score you score 2 points for a basket and 1 point for a free throw. Suppose you scored no more than 15 points in a game. How many
baskets and free throws could you have made?
a. Write a system of two inequalities that describes this situation.
2b  1 f  15 or f   f  15
b0
f 0
b. Graph the system to show all possible solutions.
c. Name a point that is a solution of the system.
(4, 4)
5. Suppose you need to use at least $1.00 worth of stamps to mail a package. You have as many $.03 stamps as you need but only four $.32 stamps. How many
of each stamp can you use?
a. Write a system of two inequalities that describes this situation.
$.03x  $.32 y  $1.00 or 100(.03 x  .32 y )  1.00(100) so 3x  32 y  100
y  4 for the four stamps you can use
b. Graph the system to show all possible solutions.
c. Name a point that is a solution of the system.
(6, 3)
and
y
3
x  100
32