name date - davis school district / overvie friends pooled the tickets they won from playing video...
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Picture ThisPicture Algebra
Vocabulary 1. Write a definition for equation in your own words.
Problem SetDraw a picture to represent each situation. Label the unknown parts with variables and the known parts
with their values. Solve the problem and write an equation to represent the situation.
1. The ages of three siblings total 21 years. The middle child is one year older than the youngest, and
the eldest is three times as old as the youngest. How old is each child?
middle:21 totalyears
youngest: y
y
yeldest:
1
y y
3y 1 y 1 1 1 y 5 21 or 5y 1 1 5 21
The youngest child is 4 years old, the middle child is 5 years old, and the eldest child is
12 years old.
Lesson 7.1 Skills Practice
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2. Carly is making three cakes for the bake sale. The second cake requires 1 __ 2
cup more flour than
the first cake. The third cake requires twice the amount of flour as the first cake. The two-pound
bag of flour she bought has 8 1 __ 2 cups—exactly the amount she needs. How much flour is needed
for each cake?
3. Of the 1850 books in the library, there are four times as many books in the fiction section as are
in the nonfiction section. Also, there are 650 more books in the reference section than are in the
nonfiction section. How many books are in each section?
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Lesson 7.1 Skills Practice page 3
Name ________________________________________________________ Date _________________________
4. Two friends pooled the tickets they won from playing video games to get a prize that requires
500 tickets. If one friend won 80 more tickets than the other friend, how many tickets did each
friend win?
5. There are 3900 workers in the three main buildings downtown. Twice as many people work in the
largest building as in the smallest of the three. There are 500 more workers in the second-largest
building than in the smallest building. How many workers are in each building?
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Lesson 7.1 Skills Practice page 4
6. Lamar, Harris, and Tyler ran a 15-mile relay race as a team. Tyler ran 3 miles farther than Harris,
and Lamar ran twice as far as Harris. How many miles was each boy’s leg of the race?
7. The Petersons set aside $500 to donate to their three favorite charities: the children’s home, the
food bank, and the animal shelter. They gave twice as much to the food bank as to the animal
shelter. Their donation to the children’s home was $50 more than the donation to the food bank.
How much did each charity receive from the Petersons?
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Lesson 7.1 Skills Practice page 5
Name ________________________________________________________ Date _________________________
8. There are 7000 middle-school students in the four middle schools in a city. There are three times
as many students at Hill Middle School than at Bell Middle School. There are twice as many
students at Ware Middle School than at Bell. Cane Middle School has 176 more students than
Ware. How many students are in each school?
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Maintaining a BalanceSolving Equations
VocabularyMatch the property of equality with its definition.
1. Addition Property of Equality
2. Subtraction Property of Equality
3. Multiplication Property of Equality
4. Division Property of Equality
a. if a 5 b, then a 1 c 5 b 1 c
b. if a 5 b, then ac 5 bc
c. if a 5 b, and c fi 0, then a __ c 5 b __ c
d. if a 5 b, then a 2 c 5 b 2 c
Problem SetDetermine what will balance one rectangle. Explain your solution. Then rewrite each representation as
an equation.
1.
I subtracted 5 squares from each side which left 2 rectangles on one side and 4 squares on
the other side. Then I divided each side by 2 which left 1 rectangle on one side and 2 squares
on the other side.
1 rectangle 5 2 squares
2x 1 5 5 9
Lesson 7.2 Skills Practice
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2.
3.
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Name ________________________________________________________ Date _________________________
4.
5.
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Lesson 7.2 Skills Practice page 4
6.
Solve each two-step equation. State the inverse operations, in the correct order of operations, you
used to isolate the variable. Check your solution.
7. 3w 2 17 5 4
Add first, and then divide. Check:
3w 2 17 5 4 3(7) 2 17 5 4
3w 2 17 1 17 5 4 1 17 21 2 17 5 4
3w 5 21 4 5 4
3w ___ 3 5 21 ___
3
w 5 7
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Lesson 7.2 Skills Practice page 5
Name ________________________________________________________ Date _________________________
8. 25 1 8x 5 65
9. 94 5 y __
4 2 18
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Lesson 7.2 Skills Practice page 6
10. g
__ 9
1 47 5 64
11. 72 5 5h 1 22
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Lesson 7.2 Skills Practice page 7
Name ________________________________________________________ Date _________________________
12. c ___ 20
2 41 5 59
13. 138 5 7h 1 5
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Lesson 7.2 Skills Practice page 8
14. 16 5 8 1 p
__ 2
Solve each riddle using equations.
15. What is a number that when you multiply it by 3 and subtract 12 from the product, you get 12?
3x 2 12 5 12
3x 5 24
x 5 8
The number is 8.
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Lesson 7.2 Skills Practice page 9
Name ________________________________________________________ Date _________________________
16. What is a number that when you multiply it by 7 and add 25 to the product, you get 46?
17. What is a number that when you multiply it by 4 and add 74 to the product, you get 90?
18. What is a number that when you multiply it by 11 and subtract 30 from the product, you get 91?
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19. What is a number that when you multiply it by 5 and add 19 to the product, you get 54?
20. What is a number that when you multiply it by 9 and subtract 63 from the product, you get 45?
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Planning a Graduation PartySolving Two-Step Equations
Vocabulary 1. Give an example of a two-step equation and describe the steps you would use to solve it.
Problem SetWrite a sentence to describe how to apply inverse operations to solve each equation. Then, solve the
equation and verify your solution.
1. 4x 1 12 5 24
First subtract 12 from each side, then divide each side by 4.
4x 1 12 5 24
4x 1 12 2 12 5 24 2 12
4x ___ 4
5 12 ___ 4
x 5 3
Verify the solution by substituting 3 for x in the equation.
4(3) 1 12 0 24
24 5 24
Lesson 7.3 Skills Practice
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Lesson 7.3 Skills Practice page 2
2. 25 2 8x 5 215
3. 13 2 x __ 7 5 6
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Lesson 7.3 Skills Practice page 3
Name ________________________________________________________ Date _________________________
4. 25x 2 12 5 18
5. x __ 9
1 29 5 41
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Lesson 7.3 Skills Practice page 4
6. 42 5 27x 1 35
7. 28 5 2x 2 14
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Lesson 7.3 Skills Practice page 5
Name ________________________________________________________ Date _________________________
8. 21 5 36 2 x ___ 30
9. 219 5 35 1 9x
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Lesson 7.3 Skills Practice page 6
10. 11x 1 13 5 29
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Lesson 7.3 Skills Practice page 7
Name ________________________________________________________ Date _________________________
Write an equation to represent each situation. Define your variables, solve the equation, and verify
your solution.
11. Ms. Moderelli charges her piano students $40 per lesson plus a semester recital fee of $55.
How many lessons did Jerry take if he paid a total of $695 for lessons this semester?
40p 1 55 5 695
Let p represent the number of lessons taken during the semester.
40p 1 55 5 695
40p 1 55 2 55 5 695 2 55
40p
____ 40
5 640 ____ 40
p 5 16
Jerry took 16 lessons.
Verify the solution by substituting 16 for p in the equation.
40(16) 1 55 0 695
695 5 695
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Lesson 7.3 Skills Practice page 8
12. The Sunshine Nursery offers a spring flower deal. If a customer purchases at least one flat of
6 annuals, they will receive 3 free perennials. How many flats of annuals must you buy to get a
total of 21 plants?
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Lesson 7.3 Skills Practice page 9
Name ________________________________________________________ Date _________________________
13. The student council ordered 1000 pencils embossed with the school name to give to honor roll
students. If they give each honor roll student two pencils and they have 840 pencils left after the
first quarter, how many students are on the honor roll in the first quarter?
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Lesson 7.3 Skills Practice page 10
14. Craig and four of his friends had a car wash to earn some extra money. They split the profits and
Craig got an extra $18 to repay his parents for the car wash supplies. If Craig got $32, how much
total money did they split among themselves?
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Lesson 7.3 Skills Practice page 11
Name ________________________________________________________ Date _________________________
15. Javier has a collection of 125 comic books. He gives each of his 3 friends the same number of
comic books and keeps his favorite 38 comic books for himself. How many comic books did he
give to each of his friends?
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Lesson 7.3 Skills Practice page 12
16. Tyler is planning a party at a restaurant. There is a flat fee of $250 to reserve the restaurant for the
evening and a charge of $20 per person for food and drink. If Tyler has $500 to spend, what is the
maximum number of people that can attend the party?
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Solving in Big-Time StyleUsing Two-Step Equations
Problem SetSolve each equation using the Distributive Property.
Lesson 7.4 Skills Practice
Name ________________________________________________________ Date _________________________
1. 6(x 1 1) 1 5 5 35
6(x 1 1) 1 5 5 35
6x 1 6 1 5 5 35
6x 1 11 5 35
6x 1 11 2 11 5 35 2 11
6x ___ 6
5 24 ___ 6
x 5 4
2. 214 5 22(5 2 x) 1 16
3. 3(2x 1 7) 2 3x 5 18 4. 0.7(x 2 2) 5 0.3
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5. 1.95(6.2 2 3x) 2 4.81 5 218.46 6. 28 5 14 1 7(x 2 6)
7. 78 5 29x 2 3(256 1 12x) 8. 0.20x 2 0.08(x 2 10) 5 24.80
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Lesson 7.4 Skills Practice page 3
Name ________________________________________________________ Date _________________________
9. 7(4x 1 9) 2 13 5 287 10. 0.25(3 2 x) 5 0.375
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Lesson 7.4 Skills Practice page 4
Write an equation to represent each situation. Define your variables and solve the equation.
11. At the Namaste Yoga Studio, the first two yoga classes you take are free with your registration fee
of $15. Each class after that is $45. How many classes can you take for $1185?
1185 5 15 1 45(x 2 2)
Let y represent the total amount paid and x represent the number of classes taken.
1185 5 15 1 45x 2 90
1185 5 45x 2 75
1185 1 75 5 45x 2 75 1 75
1260 _____ 45
5 45x ____ 45
28 5 x
You can take 28 yoga classes for $1185 dollars.
12. Clara has a coupon for $10 off at her favorite clothing store. The coupon is applied before any
discounts are taken. The store is having a sale, and offering 15% off everything. If Clara has $50
to spend, how much can her purchases total before applying the discount and her coupon?
Round to the nearest cent.
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Lesson 7.4 Skills Practice page 5
Name ________________________________________________________ Date _________________________
13. Nico bought groceries for the week. He used his debit card to pay for the groceries, including sales
tax, and added $25 cash back. If the groceries totaled $138.24 before tax, and the total debited
from his account was $173.61, what percentage was the sales tax? Round to the nearest tenth
of a percent.
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Lesson 7.4 Skills Practice page 6
14. A party store uses 20% of a tank of helium a day and fills 80 balloons. Each balloon takes
0.5 cubic feet of helium to fill. How many cubic feet of helium are in a full tank?
15. Susana bought a laptop for $500. It was marked $50 off because it was out of the box and slightly
scratched. She also got a 25% student discount, which was taken off of the original price. What
was the original price of the laptop?
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Lesson 7.4 Skills Practice page 7
Name ________________________________________________________ Date _________________________
16. A dog kennel charges $40 to board a dog for one night and $35 per night each night after that.
Henry paid a total of $215 for dog boarding. For how many nights did Henry board his dog?
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Lesson 7.5 Skills Practice
Name ________________________________________________________ Date _________________________
We’re Shipping Out!Solving and Graphing Inequalities in One Variable
VocabularyUse the words “graph,” “solve,” or “reverse” to best complete each sentence.
1. You an inequality when you determine the values of the variable that make the
inequality true.
2. You the inequality symbol when you multiply or divide each side of an
inequality by a negative value.
3. You an inequality on a number line with an open or closed circle and a ray.
Problem SetWrite an inequality for each situation.
1. Tyler needs to buy a book for school that costs $13. He also wants to get a book for each of his
two sisters and he wants to be sure he spends the same amount on each of their books. He only
has $27 to spend. Let b represent the amount he can spend on each additional book.
13 1 2b # 27
2. Ming rents a cart for her bike to carry tools and wood to school for her science project. Her
toolbox weighs 20 pounds and the cart can carry a maximum of 50 pounds. Each wood board
weighs 3 pounds. Let w represent the number of wood boards she can carry.
3. There must be less than 36 people on one bus. There are already 17 people on the bus. Let p
represent the additional number of people that can ride the bus.
4. A family of three has a coupon for $5 off their total bill when everyone orders the same meal.
The family has $40 to spend on dinner. Let m represent the cost of the meal they can order.
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Lesson 7.5 Skills Practice page 2
5. Vijay wants to keep the cost per person of his party under $15. The Party Place charges a flat fee
of $250 for an all-inclusive party. Let g represent the number of guests, including himself, he can
invite.
6. The temperature of the liquid starts at 72°F and drops 2 degrees per second. The liquid is not to
go below 40°F. Let s represent the number of seconds.
A list of possible solutions for each inequality is shown. Choose the solutions that make the inequality
true. Then, list three additional solutions to the inequality.
7. x . 2
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
The numbers 3, 4, 5, 6, and 7 make the inequality true.
Answers will vary. Three additional solutions for the inequality are 8, 9, and 10.
8. 5x , 30
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
9. 2x 1 7 $ 5
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
10. 8 # 24x
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
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Lesson 7.5 Skills Practice page 3
Name ________________________________________________________ Date _________________________
11. 3x 2 1 # 14
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
12. 4 , x __ 3 1 2
22, 21, 0, 1, 2, 3, 4, 5, 6, 7
Solve each inequality and then graph the solution.
13. 8x . 56
8x . 56
8x ___ 8
. 56 ___ 8
x . 7
0 1 2 3 4 5 6 7 8 9 10 11 12
14. 144 $ 212x
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15. 2x 1 4 # 20
16. 217 , 3 2 5x
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Lesson 7.5 Skills Practice page 5
Name ________________________________________________________ Date _________________________
17. 21 2 9x $ 26
18. 78 . 4x 1 6