Answer:
Tanya is 14; Ruby is 11.
Step-by-step explanation:
Let T represent Tanya's current age and let R represent Ruby's current age.
We know that their ages add up to 25. So:
![T+R=25](https://tex.z-dn.net/?f=T%2BR%3D25)
8 years <em>ago</em>, Tanya was twice as old as Ruby. In other words, Tanya's current age <em>minus </em>8 is the same as Ruby's current age minus 8 times 2. So:
![T-8=2(R-8)](https://tex.z-dn.net/?f=T-8%3D2%28R-8%29)
We have a system of equations. We can solve by substitution. From the first equation, subtract R from both sides:
![T=25-R](https://tex.z-dn.net/?f=T%3D25-R)
Substitute this into the second equation:
![(25-R)-8=2(R-8)](https://tex.z-dn.net/?f=%2825-R%29-8%3D2%28R-8%29)
On the left, subtract. On the right, distribute:
![17-R=2R-16](https://tex.z-dn.net/?f=17-R%3D2R-16)
Add 16 to both sides. The right side cancels:
![33-R=2R](https://tex.z-dn.net/?f=33-R%3D2R)
Add R to both sides. The left cancels:
![33=3R](https://tex.z-dn.net/?f=33%3D3R)
Divide both sides by 3:
![R=11](https://tex.z-dn.net/?f=R%3D11)
So, Ruby is currently 11 years old.
So, Tanya is currently 25-11 or 14 years old.
Check:
8 years ago, Ruby was 11-8 or 3 years old.
8 years ago, Tanya is 14-8 or 6 years old.
Tanya's age of 6 is 2 times Ruby's age of 3 so our answer is correct.