helen is now 20 years old and arlene is 10 years old. how many years ago was helen three times as...

Helen is now 20 years old and Arlene is 10 years old. How many years ago was Helen three times as old as Arlene was then?

Helen:

Arlene: 1020 20 x

10 x

ThenNow 20 3 10x x 20 30 3

20 3 30

2 20 30

2 10

5

x x

x x

x

x

x

Let represent the

number of years ago

x

5 years ago, Helen was three times as old as Arlene

Monday’s Warm Up

155

Monday’s Classwork

We are now going to set up equations for various word problems by rotating partners

There will be a Word Problem Quiz this Friday on everything up to and including

Age Problems!!!

1. The larger of two numbers is 1 less than 8 times the smaller. Their sum is 179. Find the numbers.

8 1Larger Number:

Smaller Number:

x

x

8 1 179x x

Larger Number:

Smaller Number:

179 x

x

179 8 1x x

or

2. Andy’s weight is 5 kilograms less than twice his brother’s. Together they weigh 100 kilograms. Whatare their weights? Andy's Weight:

Brother's Weight

2

5

:

x

x

2 5 100x x

Andy's Weight:

Brother's Weight:

100 x

x

100 2 5x x

or

3. The sum of three numbers is 61. The second number is 5 times the first, while the third is 2 less than the first. Find the numbers.

5 2 61x x x 1st Number:

2nd Number:

3rd Number:

5

2

x

x

x

4. Video Factory charges its members an annual fee of $16. Members can then rent movies for $2 per movie. They also allow non members to rent movies for $6 per movie. For how many movie rentals is the cost for members and non-members the same?

2 16 6x x Member Cost:

Non Member Cost:

2 1

6

6

x

x

Let represent the

number of movies rented

x

5. The sum of three numbers is 84. The second number is twice the first, and the third is 4 more than the second. Find the numbers.

2 2 4 84x x x 1st Number:

2nd Number:

3rd Number:

2

2 4

x

x

x

6. Together a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Find the cost of the table

4 4 23 562x x x Chair:

Table:

4

4 23

Lamp:

x

x

x

7. The sum of the angle measures of any triangle is 180°. Find the angle measures of a triangle if the second angle measures 10° less than twice the first, and the third angle measures 25° more than the second.

2 10 2 15 180x x x

2

1st An

10

2 15

gle:

2nd Angle:

3rd Angle:

x

x

x

8. Five times a number is the same as 22 more than three times the number. Find the number.

5 3 22x x Number: x

9. The sum of four consecutive even integers is 308. What are the integers?

2 4 6 308x x x x 1st Number:

2nd Number:

3r

2

4d Number:

4th Number: 6

x

x

x

x

10. The length of a rectangle is three times the width. If the length is increased by 4 cm and the width is decreased by 1 cm, the perimeter will be 102 cm. Find the dimensions of the original rectangle.

2 3 4 2 1 102x x Length:

Width:

3

x

x

Old New

3 4

1

x

x

11. The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total ticket sales were $1050. How many tickets of each type were sold?

2 3 400 1050x x # of Students:

# of Adults: 4 0 0

x

x

or

2 400 3 1050x x 400# of Students:

# of Adults:

x

x

12. Chickens have two feet while pigs have four feet. A pen holding only these two types of animals contains 13 animals with 44 feet. How many chickens and how many pigs are in the pen?

2 4 13 44x x # of chickens:

# of pigs: 13

x

x

or

2 13 4 44x x 13# of chickens:

# of pigs:

x

x

13. Keith weighs 20 kg more than Beth, while Henry weighs 30 kg less than twice as much as Beth. If Keith and Henry weigh the same, how much does Beth weigh (in kg)?

20 2 30x x Keith's weight:

Beth's weight:

Henry's weight:

20

2 30

x

x

x

14. Find three consecutive integers such that the sum of triple the largest and double the smallest is 13 more than six times the middle integer

3 2 2 6 1 13x x x 1st Number:

2nd Number:

3rd Number:

1

2

x

x

x

15. The length of a rectangle is five more than twice the width. If the length is decreased by 7 cm and the width is doubled, the perimeter will be 44 cm. Find the dimensions of the original rectangle

2 2 2 2 2 44x x 2 5Length:

Width:

x

x

Old New

2 2

2

x

x

16. Suppose your club is selling candles to raise money. Small candles sell for $4 a piece and large candles sell for $10 a piece. How many of each type of candle did you sell if you sold 25 candles for a total of $142?

10 4 25 142x x # of large candles:

# of small candles: 5 2

x

x

10 25 4 142x x # of large candles:

# of small candles:

25 x

x

or

17. If a touchdown is worth 7 points and a field goal is worth 3 points, how many of each did a football team have if the team scored 6 times and earned 26 points?

7 3 6 26x x # touchdowns:

# field goals: 6

x

x

or

7 6 3 26x x 6# touchdowns:

# field goals:

x

x

18. Cycle Paths, Inc. makes bicycles, tricycles, and unicycles. Last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. If they made 40 more bicycles than tricycles, how many unicycles did they make?

88 5 40x x # of bicycles:

# of tricycles:

# of unicycl s

88

5

e :

x

x

x

Monday’s Homework

Age Problems WorksheetSet up and solve each problem algebraically!!

Tuesday’s Warm UpA 23 question, 100 point exam consists of multiple choice and open ended questions. How many of each type of question are on the exam if multiple choice questions are worth 2 points each and open ended questions are worth 5 points each?

2 5 23 100x x # of Multiple Choice:

# of Open Ended: 3 2

x

x

2 23 5 100x x # of Multiple Choice:

# of Open Ended:

3

2

x

x

or

2 5 23 100x x 2 23 5 100x x

2 115 5 100

3 115 100

3 15

5

x x

x

x

x

46 2 5 100

3 46 100

3 54

18

x x

x

x

x

5 Multiple Choice

18 Open Ended

18 Open Ended

5 Multiple Choice

Tuesday’s Classwork

The sum of two numbers is 24. Seven times the smaller number is the same as 5 times the larger number. Find the smaller number.

1st Number:

2nd Numbe 4r: 2

x

x 7 5 24x x 7 120 5

12 120

10

x x

x

x

1st Number is

2nd Number i

10

s 14

Tuesday’s Classwork

An orange has 20 fewer calories than a banana. If 7 bananas have the same number of calories as 9 oranges, how many calories are in a banana?

2C 0alories per Orange:

Calories per Banana:

x

x

7 9 20x x 7 9 180

2 180

90

x x

x

x

A banana has cal90 ories

Tuesday’s Classwork

Work on today’s word problem worksheet. Review solutions at the end of the period.

8

3 3

3 3 8 15

1

1st Number:

2nd Number:

3rd Number:

1st Number is

2nd Number is

3rd Numbe

13

13

2

r is

1

36

x

x

x

x x

x

Kareem's Points:

Julius's Points:

Wilt's Points:

Kareem is

5

2 1

2 1 5 20

14

Julius

14

is

Wil

2

9

29t is

x

x

x

x x

x

Profit on Red Car:

Profit on White Car:

Profit on B

7

10

2 7 10 2

lue Car:

Profit on a Blue Car

22

$32

is

3

x

x

x

x x

x

Grok's Weight

Grok's Mother's

Weight

9

3 3 4

3

Grok NOW weighs

Mom NOW weighs

4 Last Yr This Yr

4 2 9

22

31 kg

62 kg

x x

x x

x x

x

$ of Hamburger:

$ of Hot Dog:

$ of Cheeseburge

30

20

3 2 30 2 20 7

r:

A Ham

5

95

burger cost $0.95

5

s

x

x

x

x x x

x

Length:

Width:

4

9 6

Area of Area of 96

9 4

Length of is cm

Length of is

6 Rect.#1 Re

6 96

20

24

2

ct#2

Rect#1 Rect#2

cm

Rect#1

Rect# 02

x x

x x

x

Tuesday’s Homework

Take Home Quiz

Wednesday’s Warm UpFind three consecutive even integers such that twice the sum of the second and third is 34 more than triple the first.

Mrs. Watson was 25 years old when her daughter Rose was born. Now Mrs. Watson’s age exceeds 4 times Rose’s age by 10 years. How old are they now?

Wednesday’s Warm UpFind three consecutive even integers such that twice the sum of the second and third is 34 more than triple the first.

2 2 4 3 34

2 2 6 3 34

4 12 3 34

12 34

22

x x x

x x

x x

x

x

1st Number:

2nd Number:

3rd Number:

2

4

x

x

x

1st Number is

2nd Number is

3rd Number i

22

24

s 26

Wednesday’s Warm UpMrs. Watson was 25 years old when her daughter Rose was born. Now Mrs. Watson’s age exceeds 4 times Rose’s age by 10 years. How old are they now?

Mrs. Watson's age:

Rose's age:

25

0

Then Now25 x

x

25 4 10

4 10 25

3 10 25

3 15

5

x x

x x

x

x

x

Mrs. Watson is now 30 years old and

Rose is now 5 years old

Wednesday’s Classwork

Complete the Consecutive Integer Puzzle and the Age Problem Puzzle.

Remember, Quiz Friday!!!

Thursday’s Warm Up

Complete the Age Problem Puzzle pg 50.

Remember, Quiz Friday!!!

Perimeter Challenge Question #1If one side of a square is increased by 4 inches and an adjacent side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. Find the area of the original square.

Perimeter Challenge Question #2The length of a rectangle exceeds its width by 4 feet. If the width is doubled and the length is reduced by 2 feet, a new rectangle is formed whose perimeter is 8 feet more than the perimeter of the original rectangle. Find the dimensions of the original rectangle.

Thursday’s Homework

Study For Quiz!!!