Lesson 3.7 Real-World Problems: Algebraic Reasoning

Name:

Date:

Lesson 3.7Real-World Problems: Algebraic Reasoning

Solve using algebraic reasoning.

1. Jeremy has two ropes. The longer rope is (12.5x 1 17) centimeters long, and the shorter rope is (5x 1 0.4w) centimeters long. Find the difference in length of the two ropes.

2. The radius of a circle is (7n 2 21) inches. Find the circumference of the circle in terms of n. Use 22 as an approximation for .

7

3. The average daily sales at a bookstore was (7.6k 1 2.2) dollars over a 4-day promotion. How much in total did the bookstore sell during the promotion?

4. The ratio of red ribbons to yellow ribbons is 17 to 6. If the number of red ribbons is 2m 1 5, how many ribbons are yellow?

5. During summer vacation, c children went to different destinations with their parents. 36% of the children went to Europe and 24 children to Asia. The rest of the children went to South America. How many children went to South America?

? Marshall Cavendish International (Singapore) Private Limited.

Extra Practice Course 2A49

Name:

Date:

Solve using algebraic reasoning.

6. The hourly rates for a parking garage are as follows:

First hour Each additional hour

$4.00 $3.20

Robyn parked her car in the garage for y hours. How much was her parking fee?

7. A cylinder contains (4.5x 1 2y 2 6) milliliters of liquid. How many milliliters of liquid must be added to the cylinder to make a total of (6.9x 2 3y 1 3) milliliters?

8. Among the 50 children at a book fair, b of them are boys. 30% of the girls at the book fair are younger than 12 years old while 40% of the boys are at least 12 years old. How many children at the book fair are younger than 12 years old?

9. When 2 of the koi was given away, there were still b koi and k goldfish left in

5 the pond. How many koi and goldfish were there initially?

? Marshall Cavendish International (Singapore) Private Limited.

10. The ratio of the weight of bottle A to bottle B to bottle C is 7 : 5 : 11. The total weight of bottle A and bottle C is (2x 2 9) kilograms.

a) Express the weight of bottle B in terms of x.

b) If x 5 15, find the weight of bottle B.

50Chapter 3 Lesson 3.7

? Marshall Cavendish International (Singapore) Private Limited.

12.

1

tablespoon

5

1 6

fluid

ounces

(10t

2

4)

tablespoons

5

1 6

(10t

2

4)

fluid

ounces

5

1 6

10t

2

1 6

4

5 3

t

2 3

fluid

ounces

(10t

2

4)

tablespoons

is

5 3

t

2

2 3

fluid

ounces.

11 1 w 13. Each person gets 7 notebooks.

14. Total cost of pears and apples: 0.4p 1 0.25q

15. Number of pencils:57 q There are57 q pencils.

16. Number of diners after 5 adults joined: y 1 5

Number of children:5 (y 1 5) 8

The number of children is5 (y 1 5) . 8

17. Cost of camera and lens before tax: w 1 120

Cost of camera and lens including tax:

1.08(w 1 120) 5 1.08 w 1 1.08 120

5 (1.08w 1 129.6)

Freddy paid (1.08w 1 129.6) dollars for the

camera and lens.

18.

Number

of

cards

Johnson

has:5u

2

8 13

Total number of cards that Emily and

Johnson

have:

5u

2

8 13

1

5u

5

(5u

1

5u)

2

8 13

5

10u

2

8 13

Average number of cards:

1 2

10u

8 13

1 (10u) 2

1 2

183

5u

4 13

5u 4 13

Emily and Johnson have an average of

5u

2

4 13

cards.

19. a) Total distance traveled:

140 2 1 x 1 3(2x 2 3)

14

5 140

29 14

x

1

3(2x)

1

3(23)

5 290x 1 6x 1 (29)

5 290x 1 6x 2 9

5 (296x 2 9) mi

The bullet train traveled a total of

(296x 2 9) miles.

b) When x 5 3, total distance traveled:

296x 2 9 5 296 3 2 9 5 879 mi

The total distance traveled by the bullet

train is 879 miles.

Lesson 3.7

1. Difference in length: (12.5x 1 17) 2 (5x 1 0.4w) 5 12.5x 1 17 1 (21)(5x) 1 (21)(0.4w) 5 12.5x 1 (21)(5x) 1 17 1 (21)(0.4w) 5 12.5x 2 5x 1 17 2 0.4w 5 12.5x 2 5x 1 17 2 0.4w 5 (7.5x 1 17 2 0.4w) cm The difference in length of the two ropes is (7.5x 1 17 2 0.4w) centimeters.

2. Circumference 5 2r

2

22 7

(7n

21)

44 7

(7n

21)

44 7

(7n)

44 7

(21)

44n (132)

(44n 132)in.

The circumference of the circle is (44n 2 132) inches.

3. Total sales: 4 (7.6k 1 2.2) 5 4(7.6k) 1 4(2.2) 5 (30.4k 1 8.8) dollars

The total sales during the promotion was (30.4k 1 8.8) dollars.

4. Number of yellow ribbons: 6 (2m 15) 17

6 (2m) 6 (5)

17

17

6 (2m) 6 (5) 12 m113

17

17

17

17

There are 12 m113 yellow ribbons.

17

17

5. Number of children who went to New Zealand: c 2 0.36c 2 24 5 0.64c 2 24 (0.64c 2 24) children went to New Zealand.

Extra Practice Course 2A107

6. Parking fee: 4 (1) 1 3.2(y 2 1) 5 4 1 3.2y 1 3.2(21) 5 4 1 3.2(21) + 3.2y 5 4 2 3.2 1 3.2y 5 (0.8 1 3.2y) dollars

The amount of parking fee is (0.8 1 3.2y) dollars.

7. Additional amount of liquids required: 5 (6.9x 2 3y 1 3) 2 (4.5x 1 2y 2 6) 5 6.9x 2 3y 1 3 1 (21)(4.5x) 1 (21)(2y) 1 (21)(26) 5 6.9x 1 (21)(4.5x) 2 3y 1 (21)(2y) 1 3 1 (21)(26) 5 6.9x 2 4.5x 2 3y 2 2y 1 3 1 6 5 (2.4x 2 5y 1 9) mL An additional amount of (2.4x 2 5y 1 9) milliliters of liquid is required.

8. Number of girls: 50 2 b

Number of girls younger than 12 years old: 0.3(50 2 b) 5 0.3(50) 1 0.3(2b) 5 15 2 0.3b

Number of boys younger than 12 years old: (1 2 0.4)b 5 0.6b

Number of children younger than 12 years old: (15 2 0.3b) 1 0.6b 5 15 2 0.3b 1 0.6b

5 15 1 0.3b

(15 1 0.3b) children are younger than

12 years old.

3b

9. Number of koi initially:353bb

5353bb

Number of fish initially:53533bbb 1k

3b

5355b

There were 35353535bbbb11kk ko5i and goldfish initially.

10. a) Weight o5f bottle B: 5 (2x 2 9) kg

18

b) When x 5 15, weight of bottle B:

5 (2x 9) 5 (2 159)

18

18

5 (309) 18

5 (21) 18

35 kg 6

The weight of bottle B when x 5 15 is 35 kilograms. 6

Brain@Work

1.

Second number:

5 16

15623x23x

121 2

5 16

15623x23

x

1561(56 (121) 2)

5 24

x5 x 24

145 145

5 24

x5 x 24

15 4

15 4

First number:

8 5

852542x54x

145145 33

85 852542x54x 145145 33

85 852542x54x 85 85145145 33

31 x31x 66 3 3

31 x31x 9 9

2. a) 3 of jar A 7

jar A

0.3p 1 8 7(0.3p 1 8) pints 3

The capacity of jar A is 7(0.3p 1 8) pints 3

b) 1 of jar C 2 5 2

0.3p 1 8

1 of jar C 0.3p 1 8 1 5

2

5 0.3p 1 13

jar C 2(0.3p 1 13)

5 2(0.3p) 1 2(13)

5 (0.6p 1 26) pints

The capacity of jar C is (0.6p 1 26) pints.

Chapter 4

Lesson 4.1

1. 4x 1 1 5 9 and 2x 1 1 5 5 4x 1 1 5 9

4x 1 1 2 1 5 9 2 1 4x 5 8 4x 4 4 5 8 4 4 x 5 2

Then check to see if 2 is the solution of the equation 2x 1 1 5 5. If x 5 2, 2x 1 1 5 2 2 1 1

5 5 Because the equations have same solution, they are equivalent equations.

? Marshall Cavendish International (Singapore) Private Limited.

108Answers

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download