Simple Equations

The parts of the given question are solved below:

a) The equation we have is: n + 5 = 19

Note: To check whether n = 1 satisfies the given equation, we put n = 1 in the equation.

Consider L.H.S. :

n + 5 = 1 + 5
= 6
≠ RHS

Thus, n = 1 is not a solution of the given equation.

b) The equation we have is: 7n + 5 = 19

Note: To check whether the n = -2 satisfies the given equation, we put n = -2 in the given equation.

Consider L.H.S. :

7n + 5 = 7(-2) + 5

= -9
≠ RHS

Thus, the answer is No i.e. the equation is not satisfied.

c) The equation we have is: 7n + 5 = 19

Note: To check whether the n = -2 satisfies the given equation, we put n = 2 in the given equation.

Consider L.H.S. :

7n + 5 = 7(2) + 5
= 19
= RHS

Thus, the answer is Yes i.e. the equation is satisfied.

d) The equation we have is: 4p – 3 = 13

Note: To check whether the p = 1 satisfies the given equation, we put p = 1 in the given equation.

Consider L.H.S. :

4p – 3 = 4(1) – 3

= 1

≠ RHS

Thus, the answer is No i.e. the equation is not satisfied.

e) The equation we have is: 4p – 3 = 13

Note: To check whether the p = -4 satisfies the given equation, we put p = -4 in the given equation.

Consider L.H.S. :

4p – 3 = 4(-4) – 3

= -19

≠ RHS

Thus, the answer is No i.e. the equation is not satisfied.

f) The equation we have is: 4p – 3 = 13

Note: To check whether the p = 0 satisfies the given equation, we put p = 0 in the given equation.

Consider L.H.S. :

4p – 3 = 4(0) – 3

= -3

≠ RHS

Thus, the answer is No i.e. the equation is not satisfied.

The parts of the given question are solved below:

i) The equation we have is: 5p + 2 = 17

Note: To find solution of the hit and trial method, we check for common values like -1, -2, -3 , 0 , 1 2, 3 and so on.

Lets, check for p = 1

Then, L.H.S = 5(1) + 2 = 7 ≠ RHS

So, p = 1 is not a solution of the given equation.

Now,

Check for p = 2

L.H.S = 5(2) + 2 = 12 ≠ RHS

So, p = 2 is not a solution of the given equation.

Now,

Check for p =3

L.H.S = 5(3) + 2 = 17 = RHS

So, p = 3 is a solution of the given equation.

ii) The equation we have is 3m – 14 = 4

Note: To find solution of the hit and trial method, we check for common values like -1, -2, -3, 0 , 1 2, 3 and so on.

Let us check for m = 2

Then, LHS = 3(2) – 14 = 6 – 14 = -8 ≠ RHS

So, m = 2 is not a solution of the given equation.

Now,

Let us check for m = 3

Then, LHS = 3(3) – 14 = 9 – 14 = -5 ≠ RHS

So, m = 3 is not a solution of the given equation.

Now,

Check for m = 5

LHS = 3(5) – 14 = 15 – 14 = 1 ≠ RHS

So, m = 5 is not a solution of the given equation.

Now,

Check for m = 6

LHS = 3(6) – 14 = 18 – 14 = 4 = RHS

Hence,

LHS = RHS

Therefore, m = 6 is the solution of the given equation.

The parts of the questions are solved below:

i) According to the question, the sum of numbers x and 4 is 9.

Thus, we can write the equation as,

x + 4 = 9

ii) According to the question, 2 subtracted from y is 8.

Thus, we can write the equation as

y – 2 = 8

iii) According to the question, Ten times a is 70.

Thus, we can write the equation as,

10a = 70

iv) According to the question, The number b divided by 5 gives 6.

Thus, we can write the equation as,

v) According to the question, Three-fourth of t is 15.

Thus, we can write the equation as,

vi) According to the question, Seven times m plus 7 gets you 77.

Thus, we can write the equation as,

7m+ 7 = 77

vii) According to the question, One-fourth of a number x minus 4 gives 4.

Thus, we can write the equation as,

viii) According to the question, If you take away 6 from 6 times y, you get 60.

Thus, we can write the equation as,

The parts of the given questions are solved below:

(i) According to the question, p + 4 = 15

We can write the statement as,

The sum of p and 4 is 15

(ii) According to the question, m – 7 = 3

We can write the statement as,

7 subtracted from m gives 3

(iii) According to the question, 2m = 7

We can write the statement as,

Twice of number m is 7.

(iv) According to the question,

We can write the statement as,

One fifth of m is 5

(v) According to the question,

We can write the statement as,

Three-fifth of m is 6

(vi) According to the question, 3p + 4 = 25

We can write the statement as,

Thrice of p, when added to 4 gives 25

(vii) According to the question, 4p – 2 = 18

We can write the statement as,

When 2 is subtracted from four times of p, gives 18

(viii) According to the question,

We can write the statement as,

When half of p added to 2 is 8

The parts of the given question are solved below:

(i) Let Parmit has m marbles

As per the question,

5 × (Number of marbles Parmit has) + 7 = number of marbles Irfan has

We can write this as,

5m + 7 = 37

5m = 30

m = 6

(ii) Let Laxmi be y years old

As per the question,

3 ×( Laxmi’s age) + 4 = Laxmi’s father’s age

We can write this as,

3 × y + 4 = 49

3y = 45

y = 15

(iii) Let the lowest marks be l

As per the question,

2 × (lowest marks) + 7 = Highest marks

We can write this as,

2 × l + 7 = 87

2l = 80

l = 40

(iv) Let the base angle be b

As per the question,

Vertex angle = 2 × (base angle) = 2b

Now,

Sum of interior angles of a triangle = 180

We can write this as,

b + b + 2b = 180°

4b = 180°

b = 45°

The parts of the given question are solved below:

(a) We have to separate the variables

Thus, x – 1 = 0

Now,

Adding 1 on both side of the equation,

We get,

x – 1 + 1 = 0 + 1

x = 1

(b) Here, we have to separate the variables

We have,

x + 1 = 0

Now,

Subtracting 1 on both side of the equation,

We get,

x – 1 + 1 = 0 – 1

x = -1

(c) Here, we have to separate the variables

We have,

x – 1 = 5

Now,

Adding 1 on both side of the equation,

We get,

x – 1 + 1 = 5 + 1

x = 6

(d) Here, we have to separate the variables

We have,

x + 6 = 2

Now, subtracting 6 on both side of the equation,

We get,

x + 6 - 6 = 2 – 6

x = -4

(e) Here, we have to separate the variables

We have,

y – 4 = -7

Now,

Adding 4 on both side of the equation,

We get,

x – 4 + 4 = -7 + 4

x = -3

(f) Here, we have to separate the variables

We have,

y – 4 = 4

Now,

Adding 4 on both side of the equation,

We get,

x – 4 + 4 = 4 + 4

x = 8

(g) Here, we have to separate the variables

Thus,

We have,

y + 4 = 4

Now,

Subtracting 4 on both side of the equation,

We get,

x + 4 - 4 = 4 - 4

x = 0

(h) Here,

We have to separate the variables

Thus,

We have,

y + 4 = -4

Now,

Subtracting 4 on both side of the equation,

We get,

x + 4 – 4 = -4 – 4

x = -8

The given parts of the question are solved below:

a. Here,

We have to separate the variables

Thus,

We have,

3l = 42

Dividing both sides by 3, we get,

Hence, l = 14

b. Here,

We have to separate the variables

We have,

Multiplying both sides by 2, we get

= 6 × 2

Hence,

This can be written as,

b = 12

c. Here,

We have to separate the variables

We have,

Multiplying both sides by 7, we get

×7 = 4 × 7

Hence, p = 28

d. Here,

We have to separate the variables

Thus,

We have,

4x = 25

Dividing both sides by 4, we get,

Hence, x =

e. Here,

We have to separate the variables

We have,

8y = 36

Dividing both sides by 8, we get,

Hence,

y =

f. Here,

We have to separate the variables

We have,

Multiplying both sides by 3, we get,

Hence, z =

g. Here,

We have to separate the variables

We have,

Multiplying both sides by 5, we get,

Hence, a =

h. Here,We have to separate the variables

We have,

20t = -10

Dividing both sides by 20, we get,

Hence,

t = - 1/2

The parts of the given question are solved below:

(a) Here,

We have to separate the variables

We have, 3n – 2 = 46

Adding 2 both the sides, we obtain

3n – 2 + 2 = 46 + 2

3n = 48

Dividing both sides by 3, we get,

Hence, n = 16

(b) Here,

We have to separate the variables

We have, 5m + 7 = 17

Subtracting 7 from both the sides, we obtain

5m + 7 – 7 = 17 – 7

5m = 10

Dividing both sides by 5, we get,

Hence,

m = 2

(c) Here,

We have to separate the variables

We have,

= 40

Multiplying 3 both the sides, we obtain

= 40 × 3

20p = 120

Dividing both sides by 20, we get

Hence,

This can be written as,

p = 6

(d) Here,

We have to separate the variables

We have,

Multiplying 10 both the sides, we obtain,

3p = 60

Dividing both sides by 3, we get,

Hence,

p = 20

The parts of this question are solved below:

(a) Here,

We have to find the value of p

Thus,

10p = 100

Now,

Dividing both sides by 10, we get:

=

Therefore,

p = 10

(b) Here,

We have to find the value of p

Thus,

10p + 10 = 100

10p = 100 – 10

10p = 90

Now,

Dividing both sides by 10, we get:

=

Therefore,

p = 9

(c) Here,

We have to find the value of p

Thus,

= 54

Now,

Multiplying both sides by 4, we get:

= 5 × 4

Therefore,

p = 20

(d) Here,

We have to find the value of p

Thus,

= 5

Now,

Multiplying both sides by -3, we get:

= 5 × -3

Therefore,

p = - 15

(e) Here,

We have to find the value of p

Thus,

= 6

Now,

Multiplying both sides by 4, we get:

= 6 × 4

=

Therefore,

p = 8

(f) Here,

We have to find the value of s

Thus,

3s = -9

Now,

Dividing both sides by 3, we get:

=

Therefore,

s = -3

(g) Here,

We have to find the value of s

Thus,

3s + 12 = 0

= 3s + 12 – 12 = 0 – 12

3s = -12

Now,

Dividing both sides by 3, we get:

=

Therefore,

s = -4

(h) Here,

We have to find the value of s

Thus,

3s = 0

Now,

Dividing both sides by 3, we get:

=

Therefore,

s = 0

(i) Here,

We have to find the value of q

Thus,

2q = 6

Now,

Dividing both sides by 2, we get:

=

Therefore,

q = 3

(j) Here,

We have to find the value of q

Thus,

2q – 6 + 6 = 0 + 6

2q = 6

Now,

Dividing both sides by 2, we get:

=

Therefore,

q = 3

(k) Here,

We have to find the value of q

Thus,

2q + 6 - 6 = 0 - 6

2q = - 6

Now,

Dividing both sides by 2, we get:

=

Therefore,

q = - 3

(l) Here,

We have to find the value of q

Thus,

2q + 6 - 6 = 12 - 6

2q = 6

Now,

Dividing both sides by 2, we get:

=

Therefore,

q = 3

The parts of the given question are solved below:

(a) We have,

Now,

In order to solve the given equation for y,

We will follow the following steps:

2y = 16

Now,

Dividing both sides by 2, we get:

y = 8

(b) We have,

5t + 28 = 10

Now,

In order to solve the given equation for t,

We will follow the following steps:

5t + 28 – 28 = 10 – 28

5t = - 18

Now,

Dividing both sides by 5, we get:

t =

(c) We have,

Now,

In order to solve the given equation for a,

We will follow the following steps:

Now,

Multiplying both sides by 5, we get:

Therefore,

a = -5

(d) We have,

Now,

In order to solve the given equation for q,

We will follow the following steps:

= -2

Now,

Multiplying both sides by 4, we get:

q = -8

(e) We have,

Now,

In order to solve the given equation for x,

We will follow the following steps:

Now,

Multiplying both sides by , we get:

x = -4

(f) We have,

Now,

In order to solve the given equation for x,

We will follow the following steps:

Now,

Dividing both sides by , we get:

Therefore,

x =

(g) We have,

Now,

In order to solve the given equation for m,

We will follow the following steps:

Now,

Dividing both sides by 7, we get:

m =

(h) We have,

Now,

In order to solve the given equation for z,

We will follow the following steps:

6z + 10 – 10 = -2 – 10

6z = -12

Now,

Dividing both sides by 6, we get:

Therefore,

z = -2

(i) We have,

Now,

In order to solve the given equation for t,

We will follow the following steps:

Now,

Multiplying both sides by , we get:

Therefore,t =

(j)We have,

Now,

In order to solve the given equation for y,

We will follow the following steps:

Now,

Multiplying both sides by , we get:

b = 12

The parts of the given questions are solved below:

(a) Here,

We have to solve the given equation for x.

Therefore,

We have,

2(x + 4) = 12

Dividing both sides by 2 we get,

(x + 4) =

(x + 4) = 6

⇒ x = 6 – 4

⇒ x = 2

(b) Here,

We have to solve the given equation for n.

Therefore,

We have,

3(n – 5) = 21

Dividing both sides by 3, we get:

(n – 5) =

(n – 5) = 7

⇒ n = 7 + 5

⇒ n = 12

(c) Here,

We have to solve the given equation for n.

Therefore,

We have,

3(n - 5) = -21

Dividing both sides by 3 we get,

(n - 5) =

(n – 5) = -7

n = -7 + 5

n = -2

(d) Here,

We have to solve the given equation for x.

Therefore,

We have,

-4(2 + x) = 8

Dividing both sides by -4 we get,

(2 + x) =

(2 + x) = -2

x = -2 – 2

x = -4

(e) Here,

We have to solve the given equation for x.

Therefore,

We have,

4(2 - x) = 8

Dividing both sides by 4 we get,

(2 - x) =

(2 - x) = 2

-x = 2 – 2

-x = 0

x = 0

The parts of the given question are solved below:

(a) We have to solve the given equation for p.

Therefore,

We have,

4= 5(p – 2)

Multiply 5 with both terms on RHS,

4 = 5 p - 10

Add 10 on the both sides of equation

4 + 10 = 5p -10 + 10

14 = 5p

p =

(b) We have to solve the given equation for p.

Therefore,

We have,

- 4 = 5(p – 2)

Multiply 5 with both terms on RHS,

- 4 = 5 p - 10

Add 10 on the both sides of equation

- 4 + 10 = 5p -10 + 10

6 = 5p

Dividing both sides by 5 we get,

p =

(c) We have to solve the given equation for t.

Therefore,

We have,

16 = 4 + 3(t + 2)

16 – 4 = 3(t + 2)

12 = 3(t + 2)

Dividing both sides by 3, we get,

4 = t + 2

Subtract 2 on both sides

4 - 2 = t + 2 - 2

t = 2

(d)We have to solve the given equation for p.

Therefore,

We have,

4 + 5(p - 1) = 34

4 + 5(p - 1) = 34

5(p – 1) = 34 – 4

5(p – 1) = 30

Dividing both sides by 5, we get,

p = 6 + 1

p = 7

(e) We have to solve the given equation for m

Therefore,

We have,

0 = 16 + 4(m - 6)

-16 = 4(m - 6)

Dividing both sides by 4, we get,

-4 = m - 6

- 4 + 6 = m

m = 2

The parts of the given question are solved below:

Here,

We have to frame three equations starting with x = 2

We have,

x = 2

Now,

Multiplying both sides by 5, we get:

5x = 10 (i)

Now,

Subtracting 3 from both sides, we get:

5x – 3 = 10 – 3

5x – 3 = 7 (ii)

Now,

Dividing both sides by 4, we get:

(iii)

Hence,

(i), (ii) and (iii) are the required equations.

The parts of the given question are solved below:

Here,

We have to frame three equations starting with x = -2

We have,

x = -2

Now,

Multiplying both sides by 5, we get:

5x = -10 (i)

Now,

Subtracting 3 from both sides, we get:

5x – 3 = -10 – 3

5x – 3 = -13 (ii)

Now,

Dividing both sides by 4, we get:

(iii)

Hence,

(i), (ii) and (iii) are the required equations.

The parts of this given questions are solved below:

(a) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

Eight times of a is 8a

Therefore,

As per the statement,

We can write the equation as,

8a + 4 = 60

8a = 60 – 4

8a = 56

Now,

Dividing 8 on both the sides, we get

Therefore,

a = 7

(b) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

One fifth of a is

Therefore,

As per the statement,

We can write the equation as,

= 3 + 4

= 7

Now,

Multiplying 5 to both the sides, we get

Therefore,

a = 35

(c) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

Three fourth of a is

Therefore,

As per the statement,

We can write the equation as,

= 21 – 3

= 18

Now,

Multiplying to both the sides, we get

Therefore,

a = 24

(d) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

Twice of a is 2a

Therefore,

As per the statement,

We can write the equation as,

2a – 11 = 15

2a = 15 + 11

2a = 26

Now,

Dividing 2 on both the sides, we get

Therefore,

a = 13

(e) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

Thrice of a is 3a

Therefore,

As per the statement,

We can write the equation as,

50 – 3a = 8

-3a = 8 – 50

-3a = -42

Now,

Dividing -3 on both the sides, we get

Therefore,

a = 14

(f) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

Therefore,

As per the statement,

We can write the equation as,

Now,

Multiplying 5 to both the sides, we get

Therefore,

a + 19 = 40

a = 40 – 19

a = 21

(g) We have to frame the equation on the basis of given statement

And then solve the so framed equation

Thus,

Let the number be a

We know that,

of a is

Therefore,

As per the statement,

We can write the equation as,

= 23 + 7

= 30

Now,

Multiplying to both the sides, we get

Therefore,

a = 12

The parts of the given questions are solved below:

The teacher tells the class that the highest marks obtained by the students in her class are twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

(a) Let the lowest marks be l

Therefore,

As per the question,

2 × lowest marks + 7 = Highest marks

We can write this as,

2 × l + 7 = 87

Hence,

2l + 7 = 87

2l = 87 – 7

2l = 80

l =

l = 40

Therefore,

The lowest score is 40

(b) Let us assume the base angle be b

We know that,

Sum of interior angles of a triangle is equal to 180^o

Therefore,

b + b + 40^o

2b + 40^o = 180^o

2b = 180^o – 40^o

2b = 140^o

Now,

We have to divide both sides by 2, we get

=

b = 70^o

Hence,

The base angle of the triangle is of 70^o

(c) Let us assume the score of Rahul be x

Also,

The score of Sachin = 2x

According to the condition given in the question, we have

The score of Rahul + Score of Sachin = 200 – 2

2x + x = 198

3x = 198

Now,

We have to divide both the sides by 3, we get

=

x = 66

Hence,

The score of Rahul = 66

Also,

Score of Sachin = 2 × 66 = 132

i. In the first part:

Let the marbles of Parmit be x

Now,

5 times the number of marbles Parmit has = 5x

Therefore,

According to the condition given in the question:

5x + 7 = 37

5x = 37 – 7

5x = 30

Now,

We have to divide both sides by 5, we get:

=

5x = 30

Therefore,

x = 6

(ii) Here,

As per the question,

Let Laxmi’s age be x years,

Now,

3 × Laxmi’s age + 4 = Her father’s age

We can write it as:

3x + 4 = 49

3x = 49 – 4

3x = 45

Now,

Dividing both sides by 3, we get:

Thus,

x = 15

Hence,

Laxmi’s age is 15 years

(iii) Here,

As per the question,

Let the number of fruit trees be x,

Now,

3 × number of fruit trees + 2 = Number of non-fruit trees

We can write this as,

3x + 2 = 77

3x = 77 – 2

3x = 75

Now,

Dividing both sides by 3, we get:

Thus,

x = 25

Hence,

The number of fruit trees was 25.

Let us assume the number be x

So, according to the riddle given in the question:

(7x + 50) + 40 = 300

7x + 90 = 300

7x = 300 – 90

7x = 210

Now,

We have to divide both the sides by 7

=

7x = 210

x = 30

Hence,

The required number be 30