NCERT Exercise 4.4 Solution-part2
Simple Equations 7th Math
NCERT Exercise 4.4 Solution-part2
Question(2) Solve the following
Question(2)(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?
Solution
Given, The highest score = 87
And the highest marks = twice the lowest marks + 7
Thus, lowest score = ?
Let the lowest score = p
Thus, according to question,
2p + 7 = 87
Now, after subtracting 7 from both sides, we get
⇒ 2p + 7 – 7 = 87 – 7
⇒ 2p = 80
After dividing both sides by 2, we get
⇒ 2p/2 = 80/2
⇒ p = 40
Thus, lowest score = 40 Answer
Alternate method to solve an equation
Given, The highest score = 87
And the highest marks = twice the lowest marks + 7
Thus, lowest score = ?
Let the lowest score = p
Thus, according to question,
2p + 7 = 87
After transposing 7 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +7 will become –7 when transposed to RHS
⇒ 2 p = 87 – 7
⇒ 2p = 80
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
⇒ p = 80/2
⇒ p = 40
Thus, lowest score = 40 Answer
Question(2)(b). In an isosceles triangle, the base angles are equal. The vertex angle is 400. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 1800)
Solution
Given, In an isosceles triangle, base angles are equal
And the vertex angle = 400
Sum of all the three angles of a triangle = 1800
Thus, base angle = ?
Let base angle of the given isosceles triangle = b
Now, according to question,
Vertex angle + base angle + base angle = 1800
⇒ 400 + b + b = 1800
⇒ 400 + 2b = 1800
After subtracting 400 from both sides, we get
⇒ 400 + 2b = 1800 – 400
⇒ 2b = 1400
After dividing both sides by 2, we get
⇒ 2b/2 = 140o/2
⇒ b = 700
Thus, each of the base angles = 700 Answer
Alternate method to solve an equation
Given, In an isosceles triangle, base angles are equal
And the vertex angle = 400
Sum of all the three angles of a triangle = 1800
Thus, base angle = ?
Let base angle of the given isosceles triangle = b
Now, according to question,
Vertex angle + base angle + base angle = 1800
⇒ 400 + b + b = 1800
⇒ 400 + 2b = 1800
After transposing 400 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +400 will become –400 when transposed to RHS
⇒ 2b = 1800 – 40
⇒ 2b = 1400
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
⇒ b = 140o/2
⇒ b = 700
Thus, each of the base angles = 700 Answer
Question(2)(c) Smita's mother is 34 years old. Two years from now mother 's age will be 4 times Smita's present age. What is Smita's present age?
Solution
Given, Smita's mother age = 34 years
Two years from now mother's age = Smita's present age × 4
Thus, Smita's present age = ?
Let, Smita's present age = p
And Two years now Smita's mothers age = 34 + 2
Thus, according to question,
34 + 2 = 4p
⇒ 4 p = 34+ 2
⇒ 4p= 36
After dividing both sides by 4, we get
⇒ 4p/4 = 36/4
⇒ p = 9
Thus, Smita's present age = 9 years.
Alternate method to solve an equation
Given, Smita's mother age = 34 years
Two years from now mother's age = Smita's present age × 4
Thus, Smita's present age = ?
Let, Smita's present age = p
And Two years now Smita's mothers age = 34 + 2
Thus, according to question,
34 + 2 = 4p
⇒ 4 p = 34 + 2
⇒ 4p= 36
After transposing 4 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 4 will become in division, i.e. goes to denominator after transposing to RHS
⇒ p = 36/4
⇒ p = 9
Thus, Smita's present age = 9 years Answer
Question(2)(d) 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?
Solution
Given, Score of Sachin = Twice as many runs as Rahul
Score of Sachin + Score of Rahu = 200 – 2 = 198
Thus, score of Sachin and score of Rahul = ?
Let Score of Rahul = r
Thus, Score of Sachin = 2r
Thus, according to question,
r + 2 r = 198
⇒ 3r = 198
Now, after dividing both sides by 3, we get
⇒ r = 198/3
⇒ r = 66
Thus, Score of Rahul = 66
And, since score of Sachin = 2r
Thus, score of Sachin = 2 × 66 = 132
Thus, score of Sachin = 132 and Score of Rahul = 66 Answer
Question (3) Solve the following:
Question(3)(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbels. How many marbles does Parmit have?
Solution
Given, Number of marbles Irfan has = 37
And number of marbles Irfan has = 5 × Number of marbles Parmit has + 7
Thus, Number of marbles Parmit has = ?
Let Number of marbles Parmit has = p
Now, According to question,
Number of Marbles Irfan has = 5 × Number of marbles Parmit has + 7
⇒ 37 = 5 × p + 7
⇒ 5p + 7 = 37
After subtracting 7 from both sides, we get
⇒ 5p + 7 – 7 = 37 – 7
⇒ 5p = 30
After dividing both sides by 5, we get
⇒ 5p/5 = 30/5
⇒ p = 6
Thus, number of marbles Parmit has = 6 Answer
Alternate method to solve an equation
Given, Number of marbles Irfan has = 37
And number of marbles Irfan has = 5 × Number of marbles Parmit has + 7
Thus, Number of marbles Parmit has = ?
Let Number of marbles Parmit has = p
Now, According to question,
Number of Marbles Irfan has = 5 × Number of marbles Parmit has + 7
⇒ 37 = 5 × p + 7
⇒ 5p + 7 = 37
After transposing 7 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +7 will become –7 when transposed to RHS
⇒ 5p = 37 – 7
⇒ 5p = 30
After transposing 5 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 5 will become in division, i.e. goes to denominator after transposing to RHS
⇒ p = 30/5
⇒ p = 6
Thus, Number of marbles Parmit has = 6 Answer
Question(3)(ii) Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. What is Laxmi's age?
Solution
Given, Age of Laxmi's father = 49 years
And, Age of Laxmi's father = 3 × Laxmi's age + 4
Thus, Laxmi's age = ?
Let, age of Laxmi = a years
Therefore, according to question
Age of Laxmi's father = 3 × Laxmi's age + 4
⇒ 49 years = 3a + 4
⇒ 3a + 4 = 49
After subtracting 4 from both sides, we get
⇒ 3a + 4 – 4 = 49 –4
⇒ 3a = 45
After dividing both sides by 3, we get
⇒ 3a/3 = 45/3
⇒ a = 15
Thus, Laxmi's age = 15 years Answer
(iii) Maya, Madhura and Mohsina are friends studying in the same class. In a class test in geography, Maya got 16 out of 25. Madhura got 20. Their average score was 19. How much did Mohsina score?
Solution
Given, Score of Maya = 16
Score of Madhura = 20
Average score = 19
Thus, score of Mohsina = ?
Let score of Mohsina = m
Since, average score of all the three friends = 19
Thus, total score = 3 × 19 = 57
Thus, total score = Score of Maya + Score of Madhura + Score of Mohsina
⇒ 57 = 16 + 20 + m
⇒ 16 + 20 + m = 57
⇒ 36 + m = 57
After subtracting 36 from both sides, we get
⇒ 36 + m – 36 = 57 – 36
⇒ m = 21
Thus, score of Mohsina = 21 Answer
Question (3)(iv) People of Sundargram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non fruit tress were two more than three times the number of fruit trees. What was the number of fruit trees planted?
Solution
Given, Total number of trees = 102
Number of non fruit trees = 3 × number of fruit trees + 2
Thus, number of fruit trees = ?
Let number of fruit trees = f
Thus, Number of non fruit trees = 3 × f + 2
Therefore, according to question,
Number of fruit trees + Number of non fruit trees = 102
⇒ 3f + 2 + f = 102
⇒ 4f + 2 = 102
After subtracting 2 from both sides, we get
⇒ 4f + 2 – 2 = 102 – 2
⇒ 4f = 100
After dividing both sides by 4, we get
⇒ f = 100/4
⇒ f = 25 Answer
Thus, number of fruit trees = 25 Answer
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!
Solution
According to question, A number × 7 + 50 + 40 = 300
Thus, number = ?
Let number = n
Thus, The equation is
n × 7 + 50 + 40 = 300
⇒ 7n + 90 = 300
After subtracting 90 from both sides, we get
⇒ 7n + 90 – 90 = 300 – 90
⇒ 7n = 210
After dividing both sides by 7, we get
⇒ 7n/7 = 210/7
⇒ n = 30
Thus, number = 30 Answer
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