Aftab tells his daughter,"Seven years ago,$I$ was seven times as old as you were then. Also,three years from now,$I$ shall be three times as old as you will be." Represent this situation algebraically and graphically.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Let the present age of Aftab be $x$ and the present age of his daughter be $y$.
Seven years ago:
Age of Aftab $= x - 7$
Age of his daughter $= y - 7$
According to the problem,$(x - 7) = 7(y - 7) \implies x - 7 = 7y - 49 \implies x - 7y = -42$ $...(1)$
Three years from now:
Age of Aftab $= x + 3$
Age of his daughter $= y + 3$
According to the problem,$(x + 3) = 3(y + 3) \implies x + 3 = 3y + 9 \implies x - 3y = 6$ $...(2)$
Algebraic representation:
$x - 7y = -42$
$x - 3y = 6$
For $x - 7y = -42$,we have $x = 7y - 42$:
$x$$-7$$0$$7$
$y$$5$$6$$7$

For $x - 3y = 6$,we have $x = 3y + 6$:
$x$$6$$3$$0$
$y$$0$$-1$$-2$

Explore More

Similar Questions

Two rails are represented by the equations $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$. Will the rails cross each other?

Difficult
View Solution

Form the pair of linear equations in the following problems,and find their solutions (if they exist) by the elimination method:
Five years ago,Nuri was thrice as old as Sonu. Ten years later,Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Romila went to a stationery shop and purchased $2$ pencils and $3$ erasers for ₹ $9$. Her friend Sonali saw the new variety of pencils and erasers with Romila,and she also bought $4$ pencils and $6$ erasers of the same kind for ₹ $18$. Represent this situation algebraically and graphically.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.

Solve the following pair of linear equations:
$px + qy = p - q$
$qx - py = p + q$

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo