1. 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." (Isn't this
interesting?) Represent this situation algebraically and graphically.
Answers
Step-by-step explanation:
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Step-by-step explanation:
Given :-
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."
To find :-
Represent this situation algebraically and graphically.?
Solution :-
Let the present age of Aftab be X years
Let the present age of his daughter be Y years
Then , 7 years ago Aftab's age = (X-7) years
Then , 7 years ago his daughter's age = (Y-7) years
Condition -1:-
"Seven years ago, Aftab was seven times as old as his daughter was"
=> (X-7) = 7(Y-7)
=> X-7 = 7Y-49
=> X-7-7Y+49 = 0
=> X-7Y +42 = 0-------(1)
=> X-7Y = -42 -----------(2)
And
Three years from now Aftab's age = (X+3) years
Three years from now his daughter's age = (Y+3) years
Condition-2:-
three years from now, he shall be three times as old as his daughter will be."
=> (X+3) = 3(Y+3)
=> X+3 = 3Y+9
=> X+3 -3Y-9 = 0
=> X-3Y-6 = 0------------(3)
=> X -3Y = 6 -------------(4)
On Subtracting (4) from (2)
X-7Y = -42
X -3Y = 6
(-)
___________
0-4Y = -48
____________
=> -4Y = -48
=> Y = -48/-4
=> Y = 12 years
and
On Substituting the value of Y in (4) then
X-3(12) = 6
=> X -36 = 6
=> X = 36+6
=> X = 42 years
Answer:-
Aftab's present age = 42 years
His daughter's present age = 12 years
Check :-
Aftab's present age = 42 years
His daughter's present age = 12 years
7 years ago their ages (42-7)=35 years and (12-7)=5 years
=> 35=7×5
=> Aftab's age = 7 × his daughter's age
7 years ago his age 7 times to his daughter's age .
and
3 years from now their ages (42+3)=45 years and 12+3=15 years
=> Aftab's age = 45=3×15
=> 3 × His daughters age
3 years from now his age 3 times his daughter's age
Verified the given relations in the given problem
Scale on graph:-
taking
On X- axis 1 cm = 1 unit
On Y-axis 1 cm = 1 unit
