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Answer the following:

(a) Take Sarita’s present age to be y years

(i) What will be her age 5 years from now?

(ii) What was her age 3 years back?

(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?

(iv) Grandmother is 2 years younger than grandfather. What is grandmother’s age?

(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?

(b) The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is

(c) A rectangular box has height

(d) Meena, Beena and Leena are climbing the steps to the hill top. Meena is at step

(e) A bus travels at

i) Her age 5 years from now = her present age + 5 =

ii) Her age 3 years back = her present age – 3 years =

iii) Sarita’s grandfather age = 6 times her age = 6

iv) Grandmother’s age = Grandfather’s age – 2 = 6

v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age = 5 + 3

b) breadth of the rectangular hall =

length of the hall = 4 meters less than 3 times the breadth = 3

c) height of the rectangular box =

length = 5 times the height = 5

breadth = 10 cm less than the length = 5

d) Step at which Meena is =

Step at which Beena is = Meena’s step + 8 steps =

Step at which Leena is = Meena’s step – 7 =

Total number of steps = 4

e) Distance travelled by the bus in 1 hour = v km

Distance travelled in 5 hours = 5

So, total distance from Daspur to Beespur = Distance travelled in 5 hours + 20 = 5

Change the following statements using expressions into statements in ordinary language.

(For example, Given Salim scores

(

(a) A note book costs Rs

(b) Tony puts

(c) Our class has

(d) Jaggu is

(e) In an arrangement of dots there are

a) The cost of a book is three times the cost of a notebook.

b) Tony has 8 times the number of marbles in his box than on the table.

c) Total number of students in the class is 20 times that of our class.

d) Jaggu’s uncle is 4 times the age of Jaggu and his aunt is 3 less than 4 times the age of Jaggu.

e) The total number of dots is 5 times the number of rows

(a) Given Munnu’s age to be

(Hint: Think of Mannu’s younger brother.)

Can you guess what (

(b) Given Sara’s age today to be

What will the following expression indicate?

(c) Given

a) If Munnu’s age is

(x + 4) shows that the age is 4 years older than Munnu and 3x + 7 shows that the age considered is 7 more than thrice the age of Munnu.

b) Sara’s present age = y years

y + 7 represents her future age, i.e., her age after 7 years.

y – 3 represents her past age, i.e. her age 3 years ago.

y + 4½ represents her future age, i.e. her age after 4½ years

y - 2½ represents her past age, i.e. her age 2½ years ago.

c) 2n represents twice the number of students who like football. n/2 represents half the number of students who like football.

It may represent the number of students who like cricket, or basketball etc.

State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable.

(a) 17 =

(b) (

(c) 4/2=2

(d) (7 × 3) − 19 = 8

(e) 5 × 4 − 8 = 2

(g) 2

(h) 2

(i) 7 = (11 × 5) − (12 × 4)

(j) 7 = (11 × 2) +

(k) 20 = 5

(l) 3q/2 < 5

(m)

(n) 20 − (10 − 5) = 3 × 5

(o) 7 −

Equation has = sign

While inequation as > or < sign

a) |
it an equation with one variable, x. |

b) |
it not an equation .it is an inequation. |

c) |
It is not an equation; it is a numerical equation. |

d) |
it is not an equation; it is a numerical equation. |

e) |
it is not an equation; it is an inequation. |

f) |
It is an equation with one variable, x. |

g) |
It is not an equation; it is an inequation. |

h) |
It is an equation with one variable, n. |

i) |
It is not an equation; it is a numerical equation. |

j) |
it is an equation with one variable, p. |

k) |
it is an equation with one variable, y. |

l) |
It is not an equation. It is an inequation |

m) |
It is not an equation.it is an inequation. |

n) |
It is not an equation; it is a numerical equation. |

o) |
It is an equation with one variable, x. |

Complete the entries in the third column of the table.

S. No. |
Equation |
Value of variable |
Equation satisfied Yes/No |

(a) |
10y = 80 |
y = 10 |
- |

(b) |
10y = 80 |
y = 8 |
- |

(c) |
10y = 80 |
y = 5 |
- |

(d) |
4l = 20 |
l = 20 |
- |

(e) |
4l = 20 |
l = 80 |
- |

(f) |
4l = 20 |
l = 5 |
- |

(g) |
b + 5 = 9 |
b =5 |
- |

(h) |
b + 5 = 9 |
b = 9 |
- |

(i) |
b + 5 = 9 |
b = 4 |
- |

(j) |
h − 8 = 5 |
h = 13 |
- |

(k) |
h − 8 = 5 |
h = 8 |
- |

(l) |
h − 8 = 5 |
h = 0 |
- |

(m) |
p + 3 = 1 |
p = 3 |
- |

(n) |
p + 3 = 1 |
p = 1 |
- |

(o) |
p + 3 = 1 |
p = 0 |
- |

(p) |
p + 3 = 1 |
P = − 1 |
- |

(q) |
p + 3 = 1 |
P = − 2 |
- |

S. No. |
Equation |
Value of variable |
Calculation |
Equation satisfied Yes/No |

(a) |
10y = 80 |
y = 10 |
LHS 10×10=100 RHS 80 |
No |

(b) |
10y = 80 |
y = 8 |
LHS 10×8=80 RHS 80 |
Yes |

(c) |
10y = 80 |
y = 5 |
LHS 10×5=50 RHS 80 |
No |

(d) |
4l = 20 |
l = 20 |
LHS 4×20=80 RHS 20 |
No |

e) |
4l = 20 |
l = 80 |
LHS 4×80=360 RHS 20 |
No |

(f) |
4l = 20 |
l = 5 |
LHS 4×5=20 RHS 20 |
Yes |

(g) |
b + 5 = 9 |
b =5 |
LHS 5+5=10 RHS 9 |
No |

(h) |
b + 5 = 9 |
b = 9 |
LHS 9+5=14 RHS 9 |
No |

(i) |
b + 5 = 9 |
b = 4 |
LHS 4+5=9 RHS 9 |
Yes |

(j) |
h − 8 = 5 |
h = 13 |
LHS 13-8=5 RHS 5 |
Yes |

(k) |
h − 8 = 5 |
h = 8 |
LHS 8-8=0 RHS 5 |
No |

(l) |
h − 8 = 5 |
h = 0 |
LHS 0-8=-8 RHS 5 |
No |

(m) |
p + 3 = 1 |
p = 3 |
LHS 3+3=6 RHS 1 |
No |

(n) |
p + 3 = 1 |
p = 1 |
LHS 1+3=4 RHS 1 |
No |

(o) |
p + 3 = 1 |
p = 0 |
LHS 0+3=3 RHS 1 |
No |

(p) |
p + 3 = 1 |
P = − 1 |
LHS -1+3=2 RHS 1 |
No |

(q) |
p + 3 = 1 |
P = − 2 |
LHS -2+3=1 RHS 1 |
Yes |

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

(a)

(b)

(c)

(d) q/2=7 (7, 2, 10, 14)

(e)

(f)

a) 5m = 60

Let's try the equation of each given value of m

For m = 10, 5m = 5(10) = 50

For m = 5, 5m = 5(5) = 25

For m = 12, 5m = 5(12) = 60

For m = 15, 5m = 5(15) = 75

So, we see that m = 12 satisfy the equation and is the solution.

b) n + 12 = 20

Let's try the equation of each given value of n

For n = 12, n + 12 = 12 + 12 = 24

For n = 8, n + 12 = 8 + 12 = 20

For n = 20, n + 12 = 20 + 12 = 32

For n = 0, n + 12 = 0 + 12 = 12

So, we see that n = 8 satisfy the equation and is the solution.

c) p – 5 = 5

Let's try the equation of each given value of p

For p = 0, p – 5 = 0 – 5 = -5

For p = 10, p – 5 = 10 – 5 = 5

For p = 5, p – 5 = 5 – 5 = 0

For p = -5, p – 5 = -5 – 5 = -10

So, we see that

d) q/2 = 7

Let's try the equation of each given value of q

For q = 7, q/2 = 7/2

For q = 2, q/2 = 2/2 = 1

For q = 10, q/2 = 10/2 = 5

For q = 14, q/2 = 14/2 = 7

So, we see that q = 14 satisfy the equation and is the solution.

e)

Let's try the equation of each given value of r

For

For

For

For

So, we see that

f)

Let's try the equation of each given value of x

For

For

For

For

So, we see that

(a) Complete the table and by inspection of the table, find the solution to the equation

m |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
… |

m + 10 |
− |
− |
− |
− |
− |
− |
− |
− |
− |
− |
− |

t |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
… |

5t |
− |
− |
− |
− |
− |
− |
− |
− |
− |
− |

z |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
… |

8/3 |
3 |
10/3 |
− |
− |
− |
− |
− |
− |
− |

m |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
… |

m − 7 |
− |
− |
− |
− |
− |
− |
− |
− |
− |
− |

m |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
… |

m + 10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
10 |
− |

b)

t |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
… |

5t |
15 |
20 |
25 |
30 |
35 |
40 |
45 |
50 |
55 |
− |

c)

z |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
… |

z/3 |
8/3 |
3 |
10/3 |
11/3 |
4 |
13/3 |
14/3 |
5 |
16/3 |
− |

d)

m |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
… |

m − 7 |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
− |

Solve the following riddles, you may yourself construct such riddles.

(i) Go round a square

Counting every corner

Thrice and no more!

Add the count to me

To get exactly thirty-four!

(ii) For each day of the week

Make an up count from me

If you make no mistake

You will get twenty-three!

(iii) I am a special number

Take away from me a six!

A whole cricket team

You will still be able to fix!

(iv) Tell me who I am

I shall give a pretty clue!

You will get me back

If you take me out of twenty-two!

“Counting every corner Thrice and no more!”

Implies we go around the square thrice, i.e. 12 times.

“Add the count to me to get exactly thirty-four!”

That is, when 12 is added to a number

Let us assume the number as y, we get 34.

12 +

So, 22 is the number.

If 23 is the number for Sunday,

Then counting up, Saturday is 22, Friday is 21, Thursday is 20, Wednesday is 19, Tuesday is 18, Monday is 17 and Sunday is 16.

Therefore, the number considered is 16.

Let the number be

If we take away 6 from

The special number is 17.

Let the number be x.

22 –

22 =

x = 22/2 = 11

The number is 11.

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