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# 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°. What are the base angles of the triangle? [Remember, the sum of three angles of a triangle is $180^{\circ}$].

$(c)$ 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?

**To do:**

We have to solve the given questions.

**Solution:**

(a) Highest score $=87$.

Let the lowest marks be $x$

According to question,

Highest marks obtained $= 2\times x+7$

$87=2x+7$

$87-7=2x$

$80=2x$

$x=\frac{80}{2}$

$x=40$

(b) Let one of the base angles be $b$. Since the triangle is isosceles, the other base angle will also be $b$.

Vertex angle $=40^{\circ}$.

The sum of the three angles of a triangle$=180^{\circ}$

$b+b+40^{\circ}=180^{\circ}$

$2b+40^{\circ}=180^{\circ}$

$2b=180^{\circ}-40^{\circ}$

$2b=140^{\circ}$

$b=\frac{140^{\circ}}{2}$

$b=70^{\circ}$

(c) Let Rahul's score be $x$.

This implies,

Score of Sachin $=2\times x$

$=2x$.

According to question,

$x+2x=198$ [1 century$=100$, thus, double century$=200$]

$3x=198$

$x=\frac{198}{3}$

$x=66$

So, Rahul’s score $=66$ runs

And Sachin’s score$=2x$

$=2\times66$

$=132$ runs

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