Aftab tells his daughter seven years ago I was 7 times as old as you were then. also, three years from now I shall be 3 times as old as you will be. Represent this situation algebraically and graphically.
Answers
Answer:
x=42
Step-by-step explanation:
Consider Aftab's age as x and his daughter's age as y.
Then , seven years ago,
Aftab's age =x−7
His daughter's age =y−7
i) According to the question,
x−7=7(y−7)
x−7=7y−49
x−7y=−49+7
x−7y=−42
ii) After three years,
Aftab's age =x+3
His daughter's age =y+3
According to the question,
x+3=3(y+3)
x+3=3y+9
x−3y=9−3
x−3y=6
Representing equation (i) and (ii) geometrically, we plot these equations by finding points on the lines representing these two equations
x−7y=−42⟹x=7y−42
x=7y−42 42 35 49
y 12 11 13
x−3y=6⟹x=3y+6
x=3y+6 42 36 48
y 12 10 14
From the graph we can see that two lines will intersect at a point.
x−7y=−42
x−3y=6
On subtracting the two equations, we get
4y=48
or y=12
Substituting value of y in (2),
x−36=6
∴x=42