Set up an equation in the following cases:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Prmit’s marbles.)
(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)
(iii) 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. (Take the lowest score to be l)
(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees.)
The parts of the given question are solved below:
(i) Let Parmit has m marbles
As per the question,
5 × (Number of marbles Parmit has) + 7 = number of marbles Irfan has
We can write this as,
5m + 7 = 37
(ii) Let Laxmi be y years old
As per the question,
3 ×( Laxmi’s age) + 4 = Laxmi’s father’s age
We can write this as,
3 × y + 4 = 49
(iii) Let the lowest marks be l
As per the question,
2 × (lowest marks) + 7 = Highest marks
We can write this as,
2 × l + 7 = 87
(iv) Let the base angle be b
As per the question,
Vertex angle = 2 × (base angle) = 2b
Now,
Sum of interior angles of a triangle = 180
We can write this as,
b + b + 2b = 180°