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°).

(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?

(a) Let
the lowest score be *l*.

2 × Lowest marks + 7 = Highest marks

2*l *+ 7 = 87

2*l* = 87 − 7 (Transposing 7 to R.H.S.)

2*l* = 80

Dividing both sides by 2,

Therefore, the lowest score is 40.

(b) Let
the base angles be equal to *b*.

The sum of all interior angles of a triangle is 180°.

*b* + *b* + 40° = 180°

2*b* + 40° = 180°

2*b* = 180º − 40º = 140º (Transposing 40º
to R.H.S.)

Dividing both sides by 2,

Therefore, the base angles of the triangle are of 70º measure.

(c) Let
Rahul’s score be *x*.

Therefore, Sachin’s score = 2*x*

Rahul’s score + Sachin’s score = 200 − 2

2*x* + *x* = 198

3*x* = 198

Dividing both sides by 3,

*x* = 66

Rahul’s score = 66

Sachin’s score = 2 × 66 = 132

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