Instructional Week 4: January 25-29
ISTEP + 10 Mathematics
Focus Topic: Systems of Linear Equations and Inequalities
Paced Standards:
AI.SEI.3: Write a system of two linear equations in two variables that represents a real-world problem and solve the
problem with and without technology. Interpret the solution and determine whether the solution is reasonable.+
AI.SEI.4: Represent real-world problems using a system of two linear inequalities in two variables and solve such
problems; interpret the solution set and determine whether it is reasonable. Solve other pairs of linear inequalities by
graphing with and without technology. 
PS: 1, 2, 3, 4, 5, 6, 7, and 8 +
Key Vocabulary
System of Linear Equations – a set or collection of linear equations that you deal with all together at once.
Feasible Region- set of all possible points that satisfy the inequality.
Teacher Background: Sample Problems for AI.SEI.3
1. You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog
costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total
of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas
sold. How many hot dogs were sold and how many sodas were sold? Be sure and define your variables.
Write a system of equations that represent this situation.
2. You and friend go to Taco Bell for lunch. You order three soft tacos and three burritos and your bill total is
$11.25. Your friend’s bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How
much do burritos costs? Be sure and define your variables and write a system of equations that represent
this situation.
Sample Problem Teacher Notes for AI.SEI.3
1. Let x = the number of hot dogs
Let y = the number of sodas
1.50x+.50y = 78.50
x + y = 87
x = 35 hot dogs
y = 52 sodas
You sold 35 hot dogs and 52 sodas
2. Let x = the cost of the soft tacos
Let y = the cost of burritos
3x + 3y = 11.25
4x + 2y = 10
x = 1.25 the cost of a soft taco
y = 2.5 the cost of a burritos
Each soft taco costs $1.25 and the cost of a burrito is $2.50.
Resources for AL.SEI.3
 This provides an example of a word problem and provides an explanation:
http://www.purplemath.com/modules/systprob.htm
 This provides an opportunity for students to practice online and to receive immediate feedback:
http://www.regentsprep.org/regents/math/algebra/ae3/pracword.htm
 This Khan Academy tutorial provides examples of word problems along with explanations:
https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/systems-wordproblems/e/systems_of_equations_word_problems
 This handout provides examples and includes an answer key:
http://cdn.kutasoftware.com/Worksheets/Alg1/Systems%20of%20Equations%20Word%20Problems.pdf
 This provides an explanation of how to translate a word problem into a system of equations:
http://www.shmoop.com/linear-equation-systems/translating-word-problems.html

This activity from TI incorporates the graphing calculator and provides a short video explanation
regarding systems of equations in a word problem:
http://education.ti.com/en/us/activity/detail?id=6BC31F27694F44C2B92302917F531253
Teacher Background: Sample Problems for AI.SEI.4
1. Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can hold at most
eight people. Additionally, each boat can only carry 1200 pounds of people and gear for safety reasons.
Assume on average an adult weighs 150 pounds and a child weighs 75 pounds. Also assume each group will
require 200 pounds of gear plus 10 pounds of gear per person.
Let a = number of adults
Let c = number of children
a. Write an inequality that illustrates the weight limit for a group of adults and children on the fishing boat
and a second inequality that represents the total number of passengers in the fishing boat. Graph the
solution set for this inequalities.
b. Several groups of people wish to rent a boat. Group 1 has 4 adults and 2 children. Group 2 has 3 adults
and 5 children. Group 3 has 8 adults only. Which of the groups, if any, can safely rent a boat? What
other combinations of adults and children are possible?
Sample Problem Teacher Notes for AI.SEI.4
1. a. 160a + 85c + 200 < 1200
160a + 85c <1000
a+c<8
c. Group 1: 160(4) + 85(2) + 200= 1010 which is less than or equal to 1200
Group 2: 160(3) + 85(5) + 200 = 1105 which is less than or equal to 1200
Group 3: 160(8) + 200 = 1480 which is not less than or equal to 1200
Group 1 and 2 can safely rent a boat, but Group 3 exceeds the weight limit, so cannot rent a boat.
Mark the points on the graph and show which ones fall in the feasible region and that Group 3 doesn’t
fall in the feasible region. Any combination of (c,a) that lies in the feasible region will make this system
of inequalities true.
Resources for AI.SEI.4
 This Khan Academy tutorial provides examples of word problems along with explanations:
https://www.khanacademy.org/math/algebra2/systems_eq_ineq/systems_inequalities_precalc/e/graphing_sys
tems_of_inequalities

This Learn Zillion tutorial provides an explanation of shading to find a solution to a system of
linear inequalities:
https://learnzillion.com/lessons/3078-graph-systems-of-inequalities-by-shading-their-intersection
 These handouts provide an opportunity for students to practice. Answer keys are included:
http://cdn.kutasoftware.com/Worksheets/Alg1/Systems%20of%20Inequalities.pdf
http://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Inequalities.pdf
 This provides an opportunity for students to practice online and to receive immediate feedback:
http://www.regentsprep.org/regents/math/algebra/ae9/pracgr.htm
Process Standards to Emphasize with all standards
PS.1: Make sense of problems and persevere in solving them.
PS.2: Reason abstractly and quantitatively.
PS.3: Construct a viable argument and critique the reasoning of others.
PS.4: Model with mathematics.
PS.5: Use appropriate tools strategically.
PS.6: Attend to precision.
PS.7: Look for and make use of structure.
PS.8: Look for and express regularity in repeated reasoning.
Week 4 Instructional Assessment
ISTEP+ Grade 10
Name
(AI.SEI.3) 1. The only coins that Alexis has are dimes and quarters.
 Her coins have a total value of $5.80.
 She has a total of 40 coins.
Which of the following systems of equations can be used to find the number of dimes, d, and the number
of quarters, q, Alexis has?
a.
d + q = 5.80
40d + 40q = 5.80
b. d + q = 40
0.25d + 0.10 q = 5.80
c. d + q = 5.80
0.10 d + 0.25 q = 40
d. d + q = 40
0.10d+ 0.25q = 5.80
(AI.SEI.3) 2. The Lakers scored a total of 80 points in a basketball game against the Bulls. The Lakers made a total of 37
two-point and three-point baskets. How many two-point shots did the Lakers make? How many three-point
shots did the Lakers make?
a. Define your variables.
b. Write a linear system of equations that can be used to solve this problem.
c. Solve and interpret the solution.
(AI.SEI.4) 3. Jamal can work a total of no more than 41 hours each week at his two jobs. House painting pays $5 per
hour and his sales job pays $8 per hour. He needs to earn at least $254 each week to pay his bills. Write
a system of inequalities that represents the possible numbers of hours he can work at each job.
a. Be sure and define the variables.
Let x =
Let y =
b.
Write a system of linear inequalities to represent this scenario.
c. Graph the solution set for the inequality.
d. List three possible combinations of hours Jamal could work that would allow him to pay his bills.
Solutions to Week 4 Instructional Assessment
(AI.SEI.3) 1. D
(AI.SEI.3) 2. 6 point total, 2 points per section. Use the ISTEP+ Constructed Response Rubric. Answers will vary.
a. Let x = number of two-point shots
Let y = number of three-point shots
b. x + y = 37
2x + 3y = 80
c. x = 31: y = 6
The Lakers made 31 2-point shots and 6 3-point shots.
(AI.SEI.4) 3. 8 point total, 2 points per section. Use the ISTEP+ Constructed Response Rubric. Answers will vary.
a. 2 points. Use the ISTEP+ Constructed Response Rubric.
x = number of hours of painting houses
y = number of hours of sales job
b. 2 points. Use the ISTEP+ Constructed Response Rubric.
System of Inequalities
x + y < 41
5x + 8y > 254
c. 2 points. Use the ISTEP+ Constructed Response Rubric.
d. 2 points. Use the ISTEP+ Constructed Response Rubric.
Answers will vary. The points must be in the feasible region.
All constructed response problems will be graded using the ISTEP+ Content Rubric.