How old are they now?
Elija is 2x as old as iya,iya is nineyears younger than erika,3yrs ago elijah was 2x as old as erika
- Posted:
- 3+ months ago by kendrickc...
- Topics:
- math, old, mathematician
Answers (1)
The problem has no solution, because the three relations given lead to contradiction.
Proof:
E = age of Elijah
Y = age of Iya
R = age of Erika
The relations expressed in equations are:
1) Elija is 2 times as old as Iya.
Y = E/2
2) Iya is nine years younger than Erika.
R - Y = 9
3) 3 years ago Elijah was 2 times as old as Erika.
R - 3 = (E - 3) / 2 | +3 (to make the equation express the relation as of now)
R = ((E - 3) / 2) + 3
Now, 1) and 3) describe the age of Y and R exclusively in terms of E. We can work out the difference R - Y as 1) - 3):
R - Y = ((E - 3) / 2) + 3 - E/2
R - Y = E/2 - E/2 - 3/2 +3
R - Y = 1.5
which is not even remotely as equal to 9 (as given in 2)) as you might like it to be.
Thus the contradiction is verified.
Correction: (the equations are ok.)
...
Now, 1) and 3) describe the age of Y and R exclusively in terms of E. We can work out the difference R - Y as 3) - 1):
R - Y = ((E - 3) / 2) + 3 - E/2
R - Y = E/2 - E/2 - 3/2 +3
R - Y = 1.5
which is not even remotely as equal to 9 (as given in 2)) as you might like it to be.
Thus the contradiction is verified.