EXERCISE
1. Aftab tells his daughter, "Seven years ago, I was seven times as old as you werell
Also, three years from now, I shall be three times as old as you will be.” (Isn't
interesting?) Represent this situation algebraically and graphically.
Answers
Answer:
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
According to the question,
x−7=7(y−7)
x−7=7y−49
x−7y=−49+7
x−7y=−42 …(i)
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 …(ii)
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
Answer:
Let Aftsb's age be x years
and daughter's age be y years
- x-7=7(y-7)
x-7=7y-49
7y-x = 49-7
7y-x= 42
2. x+3=3(y+3)
x+3=3y+9
3y-x= -9+3
3y-x = -6
by subtracting 2 from 1
7y-x=42
3y-x=-6
- + +
4y= 48
y=48/4
= 12 years
7y-x=42
84-x=42
-x=42-84
x= 42 years
hope this will help
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