# Ex.4.4 Q2 Simple-Equations Solution - NCERT Maths Class 7

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## Question

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?

(b) In an isosceles triangle, the base angles are equal. The vertex angle is $$40^\circ$$. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is $$180^\circ$$).

(c) Smitha’s mother is $$34$$ years old. Two years from now mother’s age will be $$4$$ times Smitha’s present age. What is Smitha’s present age?

(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?

## Text Solution

What is Known?

Statement of questions.

What is unknown?

Equation and the value of the variable.

Reasoning:

Make suitable equation using the given information and then solve the equation.

Steps:

(a) Highest score is $$87$$. Let the lowest marks be $$x$$

According to question, highest marks obtained $$= 2x + 7$$

\begin{align}87 &= 2x + 7\\87 – 7 &= 2x\\80 &= 2x\\x &= 40\end{align}

(b) Let the base angle be $$b$$. Since the triangle is isosceles, the other base angle will also be $$b$$. Vertex angle is given $$40^\circ$$.

Since, the sum of three angles of a triangle $$= 180^\circ$$

\begin{align}b + b + 40^\circ &= 180^\circ\\2b + 40^\circ &= 180^\circ\\2b = 180^\circ - 40^\circ &= 140^\circ\\b = \frac{140}{2} &= 70^\circ\end{align}

(c) Let the present age of Smitha be $$x$$. Age of her mother $$= 34$$ years

Two years from now Smitha age will be $$= x + 2$$

According to question,

\begin{align}4(x + 2) &= 34\\4x + 8 &= 34\\4x &= 34 - 8 = 16\\x &= 4\end{align}

(d) Let the score of Rahul be $$x$$, and score of Sachin be $$2x$$

According to question,

\begin{align}x + 2x &= 198\\3x &= 198\\x &= \frac{{198}}{3}= 66\end{align}

So, Rahul’s score $$= 66$$ runs

And. Sachin’s score $$= 2x = 132$$ runs

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