2.   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\degree. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180\degree).
(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?

Answers (1)

(a)    Let the lowest score be l.

Then according to the question, we have :

                                    2l\ +\ 7\ =\ 87

or                                             2l\ =\ 80

or                                               l\ =\ 40

Thus the lowest marks are 40.

 

(b)  Let the base angle of triangle is \Theta.

Then according to question, we get :

                            \Theta \ +\ \Theta\ +\ 40^{\circ}\ =\ 180^{\circ}

or                                     2\Theta\ +\ 40^{\circ}\ =\ 180^{\circ}

or                                                   2\Theta\ =\ 140^{\circ}

or                                                     \Theta \ =\ 70^{\circ}

 

(c)  Let the runs scored by Rahul is x. Then runs by Sachin is 2x.

Further, it is given that their runs fell two short of a double century.

Thus we have :                          x\ +\ 2x\ =\ 198

or                                                          3x\ =\ 198

or                                                            x\ =\ 66.

Hence runs by Rahul is 66 and runs scored by Sachin is 132.

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