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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