Exercise 4.1
"Simple Equations" Chapter 4 - Introduction - NCERT Class 7th Maths Solutions
Q 1, Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
QUESTION 1
Complete the last column of the table
| s.no | Equation | Value | Say , whether the equation is satisfied (Yes/NO) |
|---|---|---|---|
| (i) | x + 3 = 0 | x = 3 | |
| (ii) | x + 3 = 0 | x = 0 | |
| (iii) | x + 3 = 0 | x = -3 | |
| (iv) | x - 7 = 1 | x = 7 | |
| (v) | x - 7 = 1 | x = 8 | |
| (vi) | 5x = 25 | x = 0 | |
| (vii) | 5x = 25 | x = 5 | |
| (viii) | 5x = 25 | x = -5 | |
| (ix) | $\dfrac{m}{3}$ = 2 | m = -6 | |
| (x) | $\dfrac{m}{3}$ = 2 | m = 0 | |
| (xi) | $\dfrac{m}{3}$ = 2 | m = 6 |
Sol :
(i) x + 3 = 0
L.H.S. = x + 3
By putting x = 3,
L.H.S = 3 + 3 = 6 ≠ R.H.S
∴ No, the equation is not satisfied
(ii) x + 3
L.H.S. = x + 3
By putting x = 0,
L.H.S. = 0 + 3 = 3 ≠ R.H.S.
∴ No, the equation is not satisfied.
(iii) x + 3 = 0
L.H.S = x = -3
By putting x = -3,
L.H.S. = - 3 + 3 = 0 = R.H.S.
∴ Yes, the equation is satisfied.
(iv) x - 7 = 1
L.H.S. = x - 7
By putting x = 7
L.H.S. = 7 - 7 = 0 ≠ R.H.S.
∴ No, the equation is not satisfied.
(v) x - 7 = 1
L.H.S = x - 7
By putting x = 8,
L.H.S. = 8 - 7 =1 = R.H.S.
∴ Yes, the equation is satisfied.
(vi) 5x = 25
L.H.S. = 5x
By putting x = 0 ,
L.H.S. = 5 $\times$ 0 = 0 ≠ R.H.S.
∴ No, the equation is not satisfied.
(vii) 5x = 25
L.H.S. = 5x
By putting x = 5,
L.H.S. = 5 $\times$ 5 = 25 = R.H.S.
∴ Yes, the equation is satisfied.
(viii) 5x = 25
L.H.S. =5x
By putting x = -5,
L.H.S. = 5 $\times$ (-5) = -25 $\times$ R.H.S.
∴ No, the equation is not satisfied.
(ix) $\dfrac{m}{3}=2$
L.H.S = $\dfrac{m}{3}$
By putting m = -6
L.H.S $=\dfrac{-6}{3}$ = -2 ≠ R.H.S
∴ No, the equation is not satisfied. I
(x) $\dfrac{m}{3}=2$
L.H.S = $\dfrac{m}{3}$
By putting m = 0
L.H.S $\dfrac{0}{3}$ = 0 ≠ R.H.S
∴ No , the equation is not satisfied
(xi) $\dfrac{m}{3}=2$
L.H.S $=\dfrac{m}{3}$
By putting m = 6
L.H.S $=\dfrac{6}{3}$ = 2 = R.H.S
∴ Yes, the equation is satisfied.
Q 2, Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
QUESTION 2
Solve the following :
(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?
Sol :
Let the lowest score be l .
2 $\times$ Lowest marks + 7 = Highest marks
2l+7=87
2l= 87 — 7 (Transposing 7 to R.H.S.)
2l = 80
Dividing both sides by 2
$\dfrac{2l}{2}=\dfrac{80}{2}$
l = 40
Therefore , the lowest score is 40
(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angle of the triangle ? (Remember , the sum of three angles of a triangle is 180°) .
Sol :
Let the base angles be equal to b
The sum of interior angles of a triangle is 180°
b + b + 40° = 180°
2b +40° = 180°
2b = 180° - 40° (transposing 40° to RHS)
2b = 140°
Dividing both sides by 2 ,
$\dfrac{2b}{2}=\dfrac{140°}{2}$
b = 70°
Therefore, the base angles of the triangle are of 70° measure
(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?
Sol :
Let Rahul's score be x
Therefore, Sachin’s score = 2x
Rahul’s score + Sachin’s score = 200 — 2
2x + x = 198
3x = 198
$\dfrac{3x}{3}=\dfrac{198}{3}$( Dividing both sides by 3 )
x = 66
Rahul's score = 66 , Sachin's score = 2 $\times$ = 132
Q 3, Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
Solve the following:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has . Irfan has 37 marbles. How many marbles does Parmit have ?
Sol :
Let Parmit’s marbles = x
5 times the number of marbles Parmit has = 5x
5x + 7 = 37
5x = 37 — 7 (Transposing 7 to R.H.S.)
5x = 30
$\dfrac{5x}{5}=\dfrac{30}{5}$ ( Dividing both sides by 5 )
x = 6
Therefore, Parmit has 6 marbles.
(ii) Laxmi's father is 49 year old. He is 4 years older than three times Laxmi's age. What is Laxmi’s age ?
Sol :
Let Laxmi's age be x years
3 $\times$ Laxmi's age + 4 = Her father's age
3x + 4 = 49
3x = 49 - 4
3x = 45
( Dividing both sides by 3)
$\dfrac{3x}{3}=\dfrac{45}{3}$
x = 15
Therefore , Laxmi's age is 15 years
(iii) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees . The number of non-fruit trees was two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was 77?
Sol :
Let the number of fruit trees be x
3 $\times$ number of fruit trees + 2 = Number of non-fruit trees
3x + 2 = 77
3x = 77 - 2 ( Transposing 2 to R.H.S )
3x = 75
Dividing both sides of the equation by 3
$\dfrac{3x}{3}=\dfrac{75}{3}$
x = 25
Therefore , the number of fruit trees was 25
QUESTION 4
Solve the following riddle:
I am a number,
Tell my identity!
Take me seven times over
And add a fifty!
To reach a triple century
You still need forty!
Sol :
Let the number be X.
(7x + 50) + 40 = 300
7x + 90 = 300
7x = 300 — 90 (Transposing 90 to R.H.S.)
7x= 210
Diyiding both sides by 7,
$\dfrac{7x}{7}=\dfrac{210}{7}$
x = 30
Therefore , the number is 30
Q 5, Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
Write the following equations in statement forms:
(i) p + 4 = 15
Sol :
The sum of p and 4 is 1 5.
(ii) m — 7 = 3
Sol :
7 subtracted from m is 3.
(iii) 2m = 7
Sol :
Twice of a number m is 7.
(iv) $\dfrac{m}{5}=3$
Sol :
One-fifth of m is 3.
(v) $\dfrac{3m}{5}=6$
Sol :
Three-fifth of m is 6.
(vi) 3p + 4 = 25
Sol :
Three times of a number p, when added to 4, gives 25.
(vii) 4p — 2 = 18
Sol :
When 2 is subtracted from four times of a number p, it gives 18.
(viii) $\dfrac{P}{2}+2=8$
Sol :
When 2 is added to half of a number p it gives 8.
Q 6 (i, ii), Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
Q 6 (iii, iv), Ex 4.1 - Simple Equations - Chapter 4 - Maths Class 7th - NCERT
QUESTION 6
Set up an equation in the following cases:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 3 marbles. (Take m to be the number of Parmit's marbles.)
Sol :
Let Parmit has m marbles.
5×number of marbles Parmit has + 7 = Number of marbles irfan has
5×m + 7 = 37
5m + 7 = 37
(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi's age to be y years.)
Sol :
Let Laxmi be y years old.
3×Laxmi’s age + 4 = Laxmi’s father's age
3× y + 4 = 49
3y + 4 = 49
(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be I.)
Sol :
Let the lowest marks be l
2× Lowest marks + 7 = Highest marks
2×l + 7 = 87
2l + 7 = 87
(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be it in degrees. Remember that the sum of angles of a triangle is 180 degrees.)
Sol :
An isosceles triangle has two of its angles of equal measure.
Let base angle be b
Vertex angle = 2×Base angle = 2b
Sum of all interior angles of a Δ = 180°
b + b + 2b = 180°
4b = 180°
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