Name: Date: Lesson 3.7 Real-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 π.
7
© Marshall Cavendish International (Singapore) Private Limited.
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?
Extra Practice Course 2A 49
MIF_ExtraPractice C2_Ch03.indd 49
08/12/11 11:47 AM
Name: Date: Solve using algebraic reasoning.
6. The hourly rates for a parking garage are as follows:
First hour
$4.00
Each additional hour
$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
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.
© Marshall Cavendish International (Singapore) Private Limited.
5
the pond. How many koi and goldfish were there initially?
50 Chapter 3 Lesson 3.7
MIF_ExtraPractice C2_Ch03.indd 50
08/12/11 11:47 AM
1
6
1
(10t 2 4) tablespoons 5 (10t 2 4) fluid ounces
6
1
1
5  10t 2  4
6
6
12. 1 tablespoon 5 fluid ounces
5
2
 t  fluid ounces
3
3


(10t 2 4) tablespoons is  5 t 2 2  fluid ounces.
3
3
 11 1 w 
13. Each person gets  7  notebooks.


14. Total cost of pears and apples:
0.4p 1 0.25q
5
15. Number of pencils: q
7
5
There are q pencils.
7
16. Number of diners after 5 adults joined: y 1 5
5
8
Number of children: ( y 1 5)
The number of children is ( y 1 5) .
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.

8
18. Number of cards Johnson has: 5u 2 

13 
140  2
1
x 1 3(2x 2 3)
14
5 140 
29
x 1 3(2x) 1 3(23)
14
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 2r
 22 
2   (7n 21)
7
 44 
  (7n 21)
7
Total number of cards that Emily and
Johnson have: 5u 2
© Marshall Cavendish International (Singapore) Private Limited.
19.a) Total distance traveled:
8
8
1 5u 5 (5u 1 5u) 2
13
13
8
5 10u 2
13
Average number of cards:
1
8
1
1 8 
10u  (10u )  
2
13 
2
2  13 
 4
5u  
 13 
5u 4
13
Emily and Johnson have an average of

4
5u 2  cards.

13 
 44 
 44 
  (7n )   (21)
7
7
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:
There are
6
17
12
17
(2m) 6
17
13
m 1
17
( 5) 6
17
6
17
12
17
(2m 1 5)
(2m) 6
17
13
( 5)
m 1
17
yellow ribbons.
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 2A 107
MIF_ExtraPractice_C2_Ch01-Ch05_Ans.indd 107
09/12/11 5:11 PM
3
53
9.Number of koi initially: bb
353
5
bb
53
533
Number of fish initially: bbb 1 k
355
3
5
b
b
3533
 5
There were  bbb1
1kk koi and goldfish initially.
5355

b
5
10.a) Weight of5 bottle B: (2x 2 9) kg
18
b)When x 5 15, weight of bottle B:
5
18
(2 x 9 ) 5
18
5
18
5
18
35
6
(2 15 9)
(30 9)
(21)
kg
The weight of bottle B when x 5 15
is
35
6
kilograms.
Brain@Work
1.Second number:
5 52 2
 
x x 12
12
 3 3
 
16 16
5 2 
5
)
5 x2 x (5(12
16 163 3  1616 12)
5
 15 15 
x5 
24 24 x   4 4
5
15 15
x5 24 x 4
24
First number:
4
8 85 5 15 15

x
x 4   33
5 524
 24 4
8 5
15 15

8  x5 x 4   33
5 524
 24 4
8 5 
8  15  
3 3
8  x5 x 8 15
5 524
 24  5 5  4 4  1
3 3
1
9
x1
3 3x 9
x1
x6
63
3
2. a)
3
7
of jar A
jar A
0.3p 1 8
7
3
(0.3p 1 8) pints
7
The capacity of jar A is (0.3p 1 8) pints
3
b)
1
2
of jar C 2 5
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211
55
Because the equations have same solution,
they are equivalent equations.
© Marshall Cavendish International (Singapore) Private Limited.
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
3
12 years old.
b
108 Answers
MIF_ExtraPractice_C2_Ch01-Ch05_Ans_86-129.indd 108
09/12/11 1:45 AM