(f) Let us assume the required number is x.
The given above statement can be written in the equation form as,
= (x + 19)/5 = 8
Multiply both sides by 5.
= ((x + 19)/5) × 5 = 8 × 5
= x + 19 = 40
Then,
By transposing 19 from LHS to RHS, it becomes – 19
= x = 40 – 19
= x = 21
(g) Let us assume the required number is x
5/2 of the number = (5/2) x
The given above statement can be written in the equation form as,
= (5/2) x – 7 = 23
By transposing -7 from LHS to RHS, it becomes 7
= (5/2) x = 23 + 7
= (5/2) x = 30
Multiply both sides by 2,
= ((5/2) x) × 2 = 30 × 2
= 5x = 60
Then,
Divide both sides by 5.
= 5x/5 = 60/5
= x = 12
16. Solve the following.
(a) The teacher tells the class that the highest marks obtained by a student in her class are twice the lowest marks plus 7. The highest score is 87. What is the lowest score?
(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°.)
(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?
Answer:
(a) Let us assume the lowest score is x.
From the question, it is given that
The highest score is = 87
The highest marks obtained by a student in her class are twice the lowest marks plus 7= 2x + 7
5/2 of the number = (5/2) x
The given above statement can be written in the equation form as,
Then,
= 2x + 7 = Highest score
= 2x + 7 = 87
By transposing 7 from LHS to RHS, it becomes -7
= 2x = 87 – 7
= 2x = 80
Now,
Divide both sides by 2.
= 2x/2 = 80/2
= x = 40
Hence, the lowest score is 40.
(b) From the question, it is given that
We know that the sum of angles of a triangle is 180o
Let the base angle be b.
Then,
= b + b + 40o = 180o
= 2b + 40 = 180o
By transposing 40 from LHS to RHS, it becomes -40
= 2b = 180 – 40
= 2b = 140
Now,
Divide both sides by 2.
= 2b/2 = 140/2
= b = 70o
Hence, 70o is the base angle of an isosceles triangle.
(c) Let us assume Rahul’s score is x.
Then,
Sachin’s scored twice as many runs as Rahul is 2x.
Together, their runs fell two short of a double century.
= Rahul’s score + Sachin’s score = 200 – 2
= x + 2x = 198
= 3x = 198
Divide both sides by 3.
= 3x/3 = 198/3
= x = 66
So, Rahul’s score is 66.
And Sachin’s score is 2x = 2 × 66 = 132
17. 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?
(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?
(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?
Answer:
(i) Let us assume the number of Parmit’s marbles = m
From the question, it is given that
Then,
Irfan has 7 marbles, more than five times the marbles Parmit has.
= 5 × Number of Parmit’s marbles + 7 = Total number of marbles Irfan having
= (5 × m) + 7 = 37
= 5m + 7 = 37
By transposing 7 from LHS to RHS, it becomes -7
= 5m = 37 – 7
= 5m = 30
Divide both sides by 5.
= 5m/5 = 30/5
= m = 6
So, Permit has 6 marbles.
(ii) Let Laxmi’s age be = y years old
From the question, it is given that
Lakshmi’s father is 4 years older than three times her age.
= 3 × Laxmi’s age + 4 = Age of Lakshmi’s father
= (3 × y) + 4 = 49
= 3y + 4 = 49
By transposing 4 from LHS to RHS, it becomes -4
= 3y = 49 – 4
= 3y = 45
Divide both sides by 3.
= 3y/3 = 45/3
= y = 15
So, Lakshmi’s age is 15 years.
(iii) Let the number of fruit trees be f.
From the question, it is given that
3 × number of fruit trees + 2 = number of non-fruit trees
= 3f + 2 = 77
By transposing 2 from LHS to RHS, it becomes -2
=3f = 77 – 2
= 3f = 75
Divide both sides by 3.
= 3f/3 = 75/3
= f = 25
So, the number of fruit trees was 25.
18. 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!
Answer:
Let us assume the number is x.
Take me seven times over and add a fifty = 7x + 50
To reach a triple century you still need forty = (7x + 50) + 40 = 300
= 7x + 50 + 40 = 300
= 7x + 90 = 300
By transposing 90 from LHS to RHS, it becomes -90
= 7x = 300 – 90
= 7x = 210
Divide both sides by 7.
= 7x/7 = 210/7
= x = 30
Hence, the number is 30.