# Exercise 4.1

**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) | = 2 | m = -6 | |

(x) | = 2 | m = 0 | |

(xi) | = 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) 5** x **= 25

L.H.S. = 5*x*

By putting ** x** = 0 ,

L.H.S. = 5 0 = 0 ≠ R.H.S.

∴ No, the equation is not satisfied.

(vii) 5** x **= 25

L.H.S. = 5*x*

By putting ** x** = 5,

L.H.S. = 5 5 = 25 = R.H.S.

∴ Yes, the equation is satisfied.

(viii) 5** x **= 25

L.H.S. =5*x*

By putting ** x** = -5,

L.H.S. = 5 (-5) = -25 R.H.S.

∴ No, the equation is not satisfied.

(ix)

L.H.S =

By putting ** m** = -6

L.H.S = -2 ≠ R.H.S

∴ No, the equation is not satisfied. I

(x)

L.H.S =

By putting ** m **= 0

L.H.S = 0 ≠ R.H.S

∴ No , the equation is not satisfied

(xi)

L.H.S

By putting ** m** = 6

L.H.S = 2 = R.H.S

∴ Yes, the equation is satisfied.

** 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 Lowest marks + 7 = Highest marks

2** l**+7=87

2** l**= 87 — 7 (Transposing 7 to R.H.S.)

2* l *= 80

Dividing both sides by *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 ,

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 = 2*x*

Rahul’s score + Sachin’s score = 200 — 2

2x + x = 198

3x = 198

( Dividing both sides by 3 )

** x** = 66

Rahul’s score = 66 , Sachin’s score = 2 = 132

**QUESTION 3**

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 = 5*x*

5** x **+ 7 = 37

5x = 37 — 7 (Transposing 7 to R.H.S.)

5** x **= 30

( 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 Laxmi’s age + 4 = Her father’s age

3** x **+ 4 = 49

3** x **= 49 – 4

3** x** = 45

( Dividing both sides by 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 number of fruit trees + 2 = Number of non-fruit trees

3** x **+ 2 = 77

3** x** = 77 – 2 ( Transposing 2 to R.H.S )

3** x** = 75

Dividing both sides of the equation by 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.

(7** x **+ 50) + 40 = 300

7** x **+ 90 = 300

7** x **= 300 — 90 (Transposing 90 to R.H.S.)

7** x**= 210

Diyiding both sides by 7,

** x** = 30

Therefore , the number is 30

**QUESTION 5**

**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)**

Sol :

One-fifth of m is 3.

**(v)**

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)**

Sol :

When 2 is added to half of a number p it gives 8.

**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

2*l* + 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 = 2*b*

Sum of all interior angles of a Δ = 180°

b + b + 2b = 180°

4b = 180°