Question

Learning Task 3
Solve the word problems.

1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 160,
how long is each side?

2. Inzo is 10 years older than Migz. Five years ago Migs is one-third as old as
Inzo. What are their present ages?

3. An express train travels 100 kph from station A to station B. A local train travelling at 45 kph, takes 45 minutes longer for the same trip. How far apart
is station A from station B.

4. The sum of two consecutive even integers is less than 60
but greater than 24. Find at least 3 pairs of numbers.

5. The perimeter of the square is less than 152 m. Find the possible length of the
sides of the square.​

Answer 1

Answer:

Learning Task 3

Solve the word problems.

1. The sides of the quadrilateral are consecutive numbers. If the perimeter is 160,

how long is each side?

2. Inzo is 10 years older than Migz. Five years ago Migs is one-third as old as

Inzo. What are their present ages?

3. An express train travels 100 kph from station A to station B. A local train travelling at 45 kph, takes 45 minutes longer for the same trip. How far apart

is station A from station B.

4. The sum of two consecutive even integers is less than 60

but greater than 24. Find at least 3 pairs of numbers.

5. The perimeter of the square is less than 152 m. Find the possible length of the

sides of the square.

Answer 2

The sides will be: 38.5, 39.5, 40.5 and 41.5; present ages of Inzo and Migz are 20 and 10; distance between A and B is 61.36 km; 3 pairs of numbers are: 6,8; 8, 10; 10, 12, and possible sides of the square belong to the set [1, 38].

Given:

1. Perimeter of the quadrilateral with sides as consecutive numbers = 160

2. Age of Inzo = 10 years older than Migz

Age of Migz 5 years ago = 1/3rd the age of Inzo

3. Speed of express train = 100kph

speed of local train = 45kph

4. 24 < sum of two consecutive even integers < 60

5. Perimeter of square < 152

To Find:

1. sides of the quadrilateral

2. present ages of Inzo and Migz

3. distance between A and B

4. 3 pairs of numbers whose sum lies between 24 and 60

5. possible sides of the square

Solution:

1. let the sides be (x - 1), x, (x + 1) and (x + 2)

⇒ x - 1 + x + x + 1 + x + 2 = 160

4x = 158

x = 39.5

The sides will be: 38.5, 39.5, 40.5 and 41.5

2. let the ages of Inzo and Migz be x and y respectively.

x = y + 10

and (x - 5) = 3(y - 5)

⇒ (y + 10 - 5) = 3y - 15

y = 10

and x = 20

3. Let the distance between A and B be d, then-

d/100 + 45/60 = d/45

3/4 = 11d/900

d = 61.36 km

4. Let the two even integers be 2x and 2x + 2

Then, 24 < 2x + 2x + 2 < 60

5.5 < x < 14.5

Three pairs can be: 6,8; 8, 10; 10, 12

5. let the side of the square be a

Then, 4a < 152

a < 38

The possible lengths can be any number between 1 to 38

Hence, the sides will be: 38.5, 39.5, 40.5 and 41.5; present ages of Inzo and Migz are 20 and 10; distance between A and B is 61.36 km; 3 pairs of numbers are: 6,8; 8, 10; 10, 12, and possible sides of the square belong to the set [1, 38].

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