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?

Answer 1

(a) Let the lowest score be $l$.

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

$2l+7=87$

$2l=87-7$ (Transposing $7$ to R.H.S.)

$2l=80$

Dividing both sides by $2$,

$\therefore l=40$

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 $2$,

$\therefore b={70}^{\circ }$

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 $3$,

$\therefore x=66$

Rahul’s score $=66$

Sachin’s score $=2\times 66=132$