Billy is 30 years older than his son. 3 years from now, his son will be
12 of his age while his niece will be
25 of his son. Express his niece’s present age as a fraction of Billy's present age. Leave your answer in its simplest form.
| |
Billy |
Billy's son |
Billy's niece |
Difference between
Billy and Billy's son |
| Before |
10 u - 3 |
5 u - 3 |
2 u - 3 |
30 |
| Change |
+ 3 |
+ 3 |
+ 3 |
|
After
|
2x5 |
1x5 |
|
|
| |
5x1 |
2x1 |
|
Comparing Billy, his son and his niece
in the end |
10 u |
5 u |
2 u |
5 u |
The repeated identity is the age of Billy's son. LCM of 1 and 5 is 5.
The difference in age between Billy and Billy's son remains unchanged.
Difference in age between Billy and Billy's son
= 10 u - 5 u
= 5 u
5 u = 30
1 u = 30 ÷ 5 = 6
His niece's present age
= 2 u - 3
= 2 x 6 - 3
= 12 - 3
= 9
Billy's present age
= 10 u - 3
= 10 x 6 - 3
= 60 - 3
= 57
His niece's present age as a fraction of Billy's present age
=
957=
319 Answer(s):
319 
