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^o. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180^o).

(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?

The parts of the given questions are solved below:

The teacher tells the class that the highest marks obtained by the students in her class are twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

(a) Let the lowest marks be l

Therefore,

As per the question,

2 × lowest marks + 7 = Highest marks

We can write this as,

2 × l + 7 = 87

Hence,

2l + 7 = 87

2l = 87 – 7

2l = 80

l =

l = 40

Therefore,

The lowest score is 40

(b) Let us assume the base angle be b

We know that,

Sum of interior angles of a triangle is equal to 180^o

Therefore,

b + b + 40^o

2b + 40^o = 180^o

2b = 180^o – 40^o

2b = 140^o

Now,

We have to divide both sides by 2, we get

=

b = 70^o

Hence,

The base angle of the triangle is of 70^o

(c) Let us assume the score of Rahul be x

Also,

The score of Sachin = 2x

According to the condition given in the question, we have

Score of Rahul + Score of Sachin = 200 – 2

2x + x = 198

3x = 198

Now,

We have to divide both the sides by 3, we get

=

x = 66

Hence,

Score of Rahul = 66

Also,

Score of Sachin = 2 × 66 = 132