# Ex.4.1 Q6 Simple-Equations Solution - NCERT Maths Class 7

## Question

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 \(37\) marbles. (Take \(‘m’\) to be the number of Parmit’s marbles.)

(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.)

(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 \(l\).)

(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be \(b\) in degrees. Remember that the sum of angles of a triangle is \(180\) degrees).

## Text Solution

**What is unknown?**

Equations for the different statements.

**What is Known?**

Statements of the equations.

**Reasoning:**

Read the statement carefully and frame the equation.

**Steps:**

(i) Let permit has *\(m\)* number of marbles

Number of marbles Irfan has \(=5m + 7\)

Total number of marbles Irfan has \(37\)

So, \(5m + 7=37\)

(ii) Let the age of Laxmi be *\(y\)* years

Laxmi’s father is four years older than three times Laxmi’s age \(=3y + 4\)

Age of Laxmi’s father is \(49\) years

According to question,

\(3y + 4= 49\)

(iii) Let the lowest marks obtained by the student be \(l\)

Highest marks obtained by the student be \(2l + 7\)

And the highest score is \(87\)

Therefore, According to question

\(2l + 7= 87\)

(iv) Let the base angle of a triangle be *\(b\)*

Vertex angle of the triangle \(= 2b\)

According to question,

\[\begin{align}b + b + 2b = 180^\circ\\ 4b = 180^\circ\end{align}\]