question_answer 1)

Solve the following: (a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest mark 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 \[\text{4}0{}^\circ \]. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is \[\text{18}0{}^\circ \]). (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?                

Answer:

                (a) Let \['x'\] marks be the lowest score Then according to the question, we get \[2x+7=87\] \[\Rightarrow \]               \[2x=87-7\] \[\Rightarrow \]               \[x=\frac{80}{2}=40\] Therefore, the lowest score is 40 marks. (b) Let\['x'\] be the base angle of an isosceles triangle. Then according to the question, we get \[2{{x}^{\text{o}}}+{{40}^{\text{o}}}={{180}^{\text{o}}}\] \[\Rightarrow \]               \[2{{x}^{\text{o}}}={{180}^{\text{o}}}-{{40}^{\text{o}}}\] \[\Rightarrow \]               \[{{x}^{\text{o}}}=\frac{{{140}^{\text{o}}}}{2}={{70}^{\text{o}}}\] Therefore the base angles of the triangle are \[\text{7}0{}^\circ \] and \[\text{7}0{}^\circ \]. (c) Let \['x'\] runs be the score of Rahul. Then according to the question, we get                                             \[2x+x=198\] \[\Rightarrow \]               \[3x=198\] \[\Rightarrow \]               \[x=\frac{198}{3}=66\] Therefore, Rahul scores 66 runs, and Sachin scores \[\text{2}\times \text{66}=\text{132}\] runs.