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# 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?

**Solution:**

We use the concepts of simple linear equations and fundamental operations like addition, subtraction, multiplication, and division to solve the problem.

(a) Highest score is 87. Let the lowest marks be x

According to question, highest marks obtained = 2x + 7

87 = 2x + 7

87 – 7 = 2x

80 = 2x

x = 40

(b) Let the base angle be b. Since the triangle is isosceles, the other base angle will also be b.

Vertex angle is given 40°.

Since, the sum of three angles of a triangle = 180°

b + b + 40° = 180°

2b + 40° = 180°

2b = 180° − 40°

2b = 140°

b = 140°/2 = 70°

(c) Let Rahul's score be x, and score of Sachin be 2x. According to question,

x + 2x = 198 [1 century = 100, thus, 2 century = 200]

3x = 198

x = 66

So, Rahul’s score = 66 runs

and Sachin’s score = 2x = 132 runs

**☛ Check: **NCERT Solutions Class 7 Maths Chapter 4

**Video Solution:**

## 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?

NCERT Solutions for Class 7 Maths Chapter 4 Exercise 4.4 Question 2

**Summary:**

(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. The lowest score is 40 (b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. The base angles of the triangle are 70 degrees each. (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. Rahul’s score = 66 runs and Sachin’s score = 2x = 132 runs

**☛ Related Questions:**

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