Question

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 Parmit’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.)

Answer 1

(i) Let Parmit has $m$ marbles.

$5\times$ Number of marbles Parmit has $+7=$ Number of marbles Irfan has

$5\times m+7=37$

$\Rightarrow 5m+7=37$

(ii) Let Laxmi be $y$ years old.

$3\times$ Laxmi’s age $+4=$ Laxmi’s father’s age

$3\times y+4=49$

$\Rightarrow 3y+4=49$

(iii) Let the lowest marks be $l$

$2\times$ Lowest marks $+7=$ Highest marks

$2\times l+7=87$

$\Rightarrow 2l+7=87$

(iv) An isosceles triangle has two of its angles of equal measure.

Let base angle be $b$.

Vertex angle $=2\times$ Base angle $=2b$

Sum of all interior angles of a $\Delta ={180}^{\circ }$

$b+b+2b={180}^{\circ }$

$\Rightarrow 4b={180}^{\circ }$