Solve the following: (a) The teacher tells the class that the highest marks obtained by a student in her class are 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 marks be y.
According to the question, 2y+7 = 87
⇒ 2y = 87-7
⇒ 2y = 80
⇒ y = 80/2
⇒ y = 40
Thus, the lowest score is 40.

(b) Let the base angle of the triangle be b.
Given, a = 40°,b = c
Since, a+b+c = 180° [Angle sum property of a triangle]
⇒ 40°+b+b = 180°
⇒ 40° + 2b = 180°
⇒ 2b = 180°-40°
⇒ 2b = 140°
⇒ b = 140°/2
⇒ b =70°

Thus, the base angles of the isosceles triangle are 70° each.
(c) Let the score of Rahul be x runs and Sachin’s score is 2 . x
According to the question, x + 2x = 198
⇒ 3x=198
⇒ x = 198/3
⇒ x = 66
Thus, Rahul’s score = 66 runs
And Sachin’s score = 2 x 66 = 132 runs.

Class 7 Maths Chapter 4 Exercise 4.4

for more answers vist to:
https://www.tiwariacademy.com/ncert-solutions/class-7/maths/chapter-4/