Class 6 - Mathematics
Chapter - Simple Equations : Exercise 4.4
Top Block 1
Question: 1.Set up equations and solve them to find the unknown numbers in the following cases:
- Add 4 to eight times a number; you get 60.
- One-fifth of a number minus 4 gives 3.
- If I take three-fourth of a number and add 3 to it, I get 21.
- When I subtracted 11 from twice a number, the result was 15.
- Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
- Ibenhal thinks of a number. If she adds 19 to it divides the sum by 5, she will get 8.
- Answer thinks of a number. If he takes away 7 from 5⁄2 of the number, the result is 11⁄2.
Answer :
(a) Let the number be x.
According to the question, 8x + 4 = 60
⇒ 8x = 60 – 4
⇒ 8x = 56
⇒ x = 56⁄8
⇒ x = 7
(b) Let the number be y.
According to the question, y⁄5 – 4 = 3
⇒ y⁄5 = 3 + 4
⇒ y⁄5 = 7
⇒ y = 7 × 5
⇒ y = 35
(c) Let the number be z.
According to the question, (3⁄4)z + 3 = 21
⇒ (3⁄4)z = 21 – 3
⇒ (3⁄4)z = 18
⇒ 3z = 18 × 4
⇒ 3z = 72
⇒ z = 72⁄3
⇒ z = 24
(d) Let the number be x.
According to the question, 2x – 11 = 15
⇒ 2x = 15 + 11
⇒ 2x = 26
⇒ x = 26⁄2
⇒ x = 13
(e) Let the number be m.
According to the question, 50 – 3m = 8
⇒ –3m = 8 – 50
⇒ –3m = –42
⇒ m = -42⁄–3
⇒ m = 14
(f) Let the number be n.
Question: 2.Solve the following:
- 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?
- In an isosceles triangle, the base angles are equal. The vertex angle is 40o. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180o.)
- 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 the lowest marks be y.
According to the question, 2y + 7 = 87
⇒ 2y = 87 – 7
⇒ 2y = 80
⇒ y = 80⁄y
⇒ y = 40
Thus, the lowest score is 40.
(b) Let the base angle of the triangle be b.
Given, a = 40o, b = c
Since, a + b + c = 180o [Angle sum property of a triangle]
⇒ 40o + b + b = 180o
Mddle block 1
⇒ 2b = 180o – 40o
⇒ 2b = 140o
⇒ b = 140o⁄2
⇒ b = 70o
Thus, the base angles of the isosceles triangle are 70o each.
(c) Let the score of Rahul be x runs and Sachin’s score is 2x.
According to the question, x + 2x = 198
⇒ 3x = 198
⇒ x = 198⁄3
⇒ x = 66
Thus, Rahul’s score = 66 runs
And Sachin’s score = 2 x 66 = 132 runs.
Question: 3.Solve the following:
- 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?
- Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?
- People of Sundergram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted?
Answer :
(i) Let the number of marbles Parmit has be m.
According to the question, 5m + 7 = 37
⇒ 5m = 37 – 7
⇒ 5m = 30
⇒ m = 30⁄5
⇒ m = 6
Thus, Parmit has 6 marbles.
(ii) Let the age of Laxmi be y years.
Then her father’s age = (3y + 4) years
According to question, 3y + 4 = 49
⇒ 3y = 49 – 4
⇒ 3y = 45
⇒ y = 45⁄3
⇒ y = 15
Thus, the age of Laxmi is 15 years.
(iii) Let the number of fruit trees be t.
Then the number of non-fruits tree = 3t + 2
According to the question, t + 3t + 2 = 102
⇒ 4t + 2 = 102
⇒ 4t = 102 – 2
⇒ 4t = 100
⇒ t = 100⁄4
⇒ t = 25
Thus, the number of fruit trees are 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!
Answer :
Let the number be n.
According to the question, 7n + 50 + 40 = 300
⇒ 7n + 90 = 300
⇒ 7n = 300 – 90
⇒ 7n = 210
⇒ n = 210⁄7
⇒ n =3 0
Thus, the required number is 30.