a mother is three times as old as her daughter is now six years ago the product of their age was 180 find their present age
Answers
Step-by-step explanation:
Given :-
A mother is three times as old as her daughter is now six years ago the product of their age was 180.
To find :-
Find their present age ?
Solution :-
Let the present age of the daughter be X years
The present age of the mother = Three times the daughter's age
= 3X years
Six years ago,
Mother's age = (3X-6) years
Her daughter's age = (X-6) years
The product of their ages
= (X-6)×(3X-6)
=> X(3X-6)-6(3X-6)
=> 3X²-6X-18X+36
=> 3X²-24X+36
According to the given problem
The product of their ages six years ago = 180
=> 3X²-24X+36 = 180
=> 3(X²-8X+12) = 180
=> X²-8X+12 = 180/3
=> X²-8X+12 = 60
=> X²-8X+12-60 = 0
=> X²-8X-48 = 0
=> X²+4X-12X-48 = 0
=> X(X+4)-12(X+4) = 0
=> (X+4)(X-12) = 0
=> X+4 = 0 or X-12 = 0
=> X = -4 or X = 12
X can not be negative.
So, X = 12 years
Daughter's age = 12 years
3X = 3×12 = 36 years
Mother's age = 36 years
Answer:-
The present age of daughter = 12 years
The present age of mother = 36 years
Check :-
Daughter's age = 12 years
Mother's age = 36 years
=> 3×12 years
=> 3× Daughter's age
and
6years ago
Daughter's age = 12-6 = 6 years
Mother's age = 36-6 = 30 years
Product of their ages = 6×30 = 180 years
Verified the given relations in the given problem.