Billy is 40 years older than his daughter. 8 years from now, his daughter will be
12 of his age while his niece will be
25 of his daughter. Express his niece’s present age as a fraction of Billy's present age. Leave your answer in its simplest form.
|
Billy |
Billy's daughter |
Billy's niece |
Difference between Billy and Billy's daughter |
Before |
10 u - 8 |
5 u - 8 |
2 u - 8 |
40 |
Change |
+ 8 |
+ 8 |
+ 8 |
|
After
|
2x5 |
1x5 |
|
|
|
5x1 |
2x1 |
|
Comparing Billy, his daughter and his niece in the end |
10 u |
5 u |
2 u |
5 u |
The repeated identity is the age of Billy's daughter. LCM of 1 and 5 is 5.
The difference in age between Billy and Billy's daughter remains unchanged.
Difference in age between Billy and Billy's daughter
= 10 u - 5 u
= 5 u
5 u = 40
1 u = 40 ÷ 5 = 8
His niece's present age
= 2 u - 8
= 2 x 8 - 8
= 16 - 8
= 8
Billy's present age
= 10 u - 8
= 10 x 8 - 8
= 80 - 8
= 72
His niece's present age as a fraction of Billy's present age
=
872=
19 Answer(s):
19