Solve the following: (a) The teacher tells the class that the highest marks obtained by a student in her class - Maths - Simple Equations

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 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?

Gopal Mohanty · Accepted Answer

(a) Let the lowest score be l 2 × Lowest marks + 7 = Highest marks 2l + 7 = 87 2l = 87 − 7 (Transposing 7 to R H S ) 2l = 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° 2b + 40° = 180° 2b = 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 = 2x Rahul’s score + Sachin’s score = 200 − 2 2x + x = 198 3x = 198 Dividing both sides by 3,

x = 66 Rahul’s score = 66 Sachin’s score = 2 × 66 = 132