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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 angle 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?



Answer -

(a) Let the lowest score be x.
Step I: Highest marks obtained = 2x + 7
Step II: 2x + 7 = 87 is the required equation. Solving the equation, we have
2x + 7 = 87
⇒ 2x = 87 – 7 (Transposing 7 to RHS)
⇒ 2x = 80
⇒ 2x/2=80/2 (Dividing both sides by 2)
⇒ x = 40 is the required lowest marks.
(b) Let each base angle be x degrees.
Step I: Sum of all angles of the triangle (x + x + 40) degrees.
Step II: x + x + 40 = 180°
⇒ 2x + 40° = 180°
Solving the equation, we have
2x + 40° = 180°
2x = 180° – 40° (Transposing 40° to RHS)
2x = 140°
⇒ 2x/2=140/2 (Dividing both sides by 2)
⇒ x = 70°
Thus the required each base angle = 70°
(c) Let the runs scored by Rahul = x
Runs scored by Sachin = 2x
Step I: x + 2x = 3x
Step II: 3x + 2 = 200
Solving the equation, we have
3x + 2 = 200
⇒ 3x = 200 – 2 (Transposing 2 to RHS)
⇒ 3x = 198
⇒ 3x/3=198/3 (Dividing both sides by 3)
⇒ x = 66
Thus, the runs scored by Rahul is 66 and the runs scored by Sachin = 2 × 66 = 132

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