Math 3 Unit 1 Homework Packet
Homework 1-1
I.
Solve each linear equation. MUST SHOW WORK!
1) 𝟕𝐰 + 𝟐 = 𝟑𝐰 + 𝟑𝟎
2) 𝟐 − 𝟑(𝒙 + 𝟒) = 𝟖
4)
𝟑𝒃−𝟒
𝟒𝒃+𝟏
𝟐
=𝟑
𝟓
𝟑
𝟏
𝟖
𝟒
𝟏𝟔
7) + 𝒙 =
10) 𝟑(𝟐𝒛 + 𝟐𝟓) − 𝟐(𝒛 − 𝟏) = 𝟕𝟖
3) 𝟔𝒙 − 𝟏𝟐 + 𝟐𝒙 = 𝟑 + 𝟖𝒙 − 𝟏𝟓
5) 𝟕(𝒂 + 𝟏) − 𝟑𝒂 = 𝟓 + 𝟒(𝟐𝒂 − 𝟏)
6) 𝟒(𝒘 − 𝟏) + 𝟑 = 𝟒𝒘 − (𝒘 + 𝟏)
8) 𝟑(𝟑 − 𝒑) − 𝟑𝒑 = 𝟐(𝟑 − 𝟑𝒑) − 𝟑
9) 𝟒 − ( 𝒙 + ) = 𝒙
11) 𝟕𝒂 − 𝟒(𝟐𝒂 − 𝟖) = 𝟓(𝟒 − 𝒂) − 𝟒
12. Solve for m in 𝒎𝒙 + 𝒃𝒚 = 𝒄
𝟏 𝟏
𝟐
𝟓
𝟐 𝟑
𝟑
𝟑
1
Homework 1-2:
Linear Functions and Inequalities
Show all work on notebook paper!!!
1. Tim earns $7 an hour working at McDonald’s. He also was given a signing bonus when he started of $25. Write an
equation that represents Tim’s salary at McDonald’s.
2. A pool is being drained such that the amount of water (in gallons) at any given time (in min) can be found by 𝑦 =
20000 − 400𝑥.
a. What is the slope and what does the slope mean in terms of this application?
b. What is the y-intercept and what does it represent in this application?
c. What is the x-intercept and what does it represent in this application?
Given the following equations, find the slope, y-intercept, and graph on separate paper.
2.
𝑦 = 2𝑥 + 3
4. 3𝑥 − 4𝑦 = 12
5. 𝑥 = 4
6. 𝑦 + 3 = 0
Graph following linear inequalities:
7. 𝑦 < −2𝑥 + 3
1
2
8. 𝑦 ≥ 𝑥 − 4
9. 3𝑥 − 2𝑦 ≥ 10
10. 𝑥 > −3
11. Write an equation in slope intercept form that passes through (-10, 3) and (-2, -5).
1
12. Write an equation that passes through (9,-1) and is parallel to 𝑦 = − 3 𝑥 − 6.
13. Write an equation that passes through (-12, 2) and is perpendicular to y 
3
x2
4
14. Write the equation in slope intercept form that has a y int at (0,3) and is parallel to 3x+y=8
15. Write the equation in slope intercept form that has a y int at (0,-1) and is perpendicular to y=-5x+7
16. Write the equation in slope int form that is perpendicular to 4x-y-3=0 and having the same y int.
2
Homework 1-3:
1. x  y  4
y  3x  4
 2x  y  1
6. 3x  3 y  12
10. x  2 y  13
 4x  2 y  2
4 x  2 y  18
4. x  2 y  2
x  2 y  1
7. 4 y  4 x  4
8. 2 x  6 y  2
 x  y  1
x  3 y  13
 2 x  2 y  8
3x  2 y  8
9. y  2 x  1
3.  x  4 y   27
2. 2 x  y  17
 x  2 y  13
5. 1 x  y   8
2
Solve the System using Substitution or Elimination
11. 1 x  3 y  2
4
12.  1 x  y   8
2
x  12 y  8
 3x  y   3
14. Graph the system of inequalities.
15. Graph the system of inequalities.
3x + 9y > 27
7x + 5y < 35
4x -2y ≤ 12
8x – 7y ≤ 56
2x + 3y > -12
5x – 3y ≥ -15
Homework 1-4
Solve the system using the elimination method.
1. x  6 y  2 z  5
2. x  y  z   2
2x  3y  z  4
2x  y  z  8
3x  4 y  z   2
 x  2 y  2 z  10
3. Three bouquets of flowers are ordered at a florist. Three roses, 2 carnations, and 1 tulip cost
$14, 6 roses, 2 carnations, and 6 tulips cost $38, and 1 rose, 12 carnations, and 1 tulip cost $18.
How much does each item cost?
Solve the system of linear equations using the substitution/elimination method.
4. y   3
5. x  y  5
2x  y  5
 x  4 y  2z  3
x  2y  z  6
 x  3 y  5z   6
3
Homework 1-5
Solve the system using matrices.
1. 3x  y  z  1
2. 4 x  3 y  5 z   9
3.
2x  y  6
3x  2 y  5 z  16
6 x  6 y  3z  6
4 x  3 y  2 z  14
3x  3 y  2 z  6
3x  3 y  4 z  19
 x  2 y  3z  12
4. Your friend claims that she has a bag of 30 coins containing nickels, dimes, and quarters. The
total value of the 30 coins is $3. There are twice as many nickels as there are dimes. Is your
friend correct? Explain your reasoning.
5 . Find the measures of the angles marked
x, y, and z in the triangle.
5)
4
Homework 1-6
5
Homework 1-7
State the variables, the objective function, and the constraints. Graph the system of inequalities on GRAPH PAPER, find
your feasible region, list the points of your feasible region and then optimize your solution. Answer the extension
questions after each problem. SHOW ALL WORK ON PAPER!
1. Emilio has a small carpentry shop in his basement to make bookcases. He makes two sizes, large and small. His profit
on a large bookcase is $80.00, and his profit on a small bookcase is $50.00. It takes Emilio 6 hours to make a large
bookcase and 2 hours to make a small one. He can spend only 24 hours each week on his carpentry work. He must make
at least two of each size each week. What is the maximum weekly profit? How many of each size bookcase should be
made?
Variables:
Objective
Function:
Constraints:
Points of feasible region and
solutions:
Answer in complete
sentence:
x =
y=
a) In his optimal plan, did he use all his hours available? If not, how many hours did he have left unused?
b) Did he make the desired number of bookcases? If he made more than desired, how many more bookcases did he
make?
2. The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at
most 200 units of paper a day. At least 10 units of notebook paper and 80 units of newsprint are required daily by regular
customers. If profit on notebook paper is $500 per unit and profit on newsprint is $350 per unit, how much should the
manager have the mill produce to maximize his profits? How many units of notebook paper and how many units of newsprint
must be produced to maximize profits?
Variables:
x =
Objective
Constraints:
Function:
Points of feasible region and
Answer in complete
solutions:
sentence:
y=
3. A small company produces knitted Afghans and sweaters and sells them through a chain of specialty stores. The
company is to supply the stores with a total of no more than 100 Afghans and sweaters per day. The stores guarantee that
they will sell at least 10 and no more than 60 Afghans per day and at least 20 sweaters per day. The company makes a profit
of $10 on each afghan and a profit of $12 on each sweater. How many of each should the company produce to maximize
profit?
Variables:
x =
Objective
Function:
Constraints:
Points of feasible region and
Answer in complete
solutions:
sentence:
y=
6
Homework 1-8
State the variables, the objective function, and the constraints. Graph the system of inequalities on GRAPH PAPER, find
your feasible region, list the points of your feasible region and then optimize your solution. Answer the extension
questions after each problem. SHOW ALL WORK ON PAPER!
1) As a receptionist for a veterinarian, one of Dolores Alvarez’s tasks is to schedule appointments. She allots 20 minutes
for a routine office visit and 40 minutes for a surgery. The veterinarian cannot do more than 6 surgeries per day. The
office has 7 hours available for appointments. If an office visit costs $55 and most surgeries cost $125, find a
combination of office visits and surgeries that will maximize the income the veterinarian practice receives per day.
Variables:
x =
Objective
Function:
Constraints:
Points of feasible region and
solutions:
Answer in complete
sentence:
y=
2) A farmer decides to plant alfalfa and corn. Alfalfa requires 2 hours per ton to harvest while corn required 3 hours. The
harvesting time available is 1200 hours. Each crop requires 1 hour to plant and the total planting time available is 500
hours. The farmer will make a profit of $250 for every ton of alfalfa and $350 for each ton of corn harvested. How
much of each crop should the farmer plant to maximize her profit?
Variables:
x =
Objective
Function:
Constraints:
Points of feasible region and
solutions:
Answer in complete
sentence:
y=
3) The Oklahoma City division of SuperSport Inc produces footballs and basketballs. It takes 4 hours on Machine A and
2 hours on machine B to make a football. Producing a basketball requires 6 hours on machine A, 6 hours on machine
B, and 1 hour on machine C. Machine A can run no more than 120 hours a week, machine B is available 72 hours a
week, and machine C is available 10 hours per week. If the company makes $3 profit on each football and $2 profit on
each basketball, how many of each should they make to maximize their profit?
Variables:
x =
Objective
Function:
Constraints:
Points of feasible region and
solutions:
Answer in complete
sentence:
y=
7