Answer: Maggie is currently 10 years old.
====================================================
Step-by-step explanation:
M = Maggie's age today
S = Steven's age today
The ratio of their current ages, specifically Maggie's age to Stevens age, is 2:3. So 2/3 = M/S
We can cross multiply to get 2S = 3M and divide both sides by 2 getting S = 3M/2 = 1.5M
So whatever Maggie's age is, we multiply by 1.5 to get Steven's age. This only applies to their current present day ages.
----------------------
In 10 years, Maggie will be M+10 years old and Steven will be S+10 years old.
The ratio of their ages at this point in time is 4:5, so,
4/5 = (M+10)/(S+10)
4(S+10) = 5(M+10) ..... cross multiply
4S+40 = 5M+50
4S-5M = 50-40
4S-5M = 10
4(1.5M) - 5M = 10 .... plug in S = 1.5M
6M - 5M = 10
M = 10
Maggie is currently 10 years old.
----------------------
Extra info:
Use the value of M to find S.
S = 1.5*M
S = 1.5*10
S = 15
So Steven is currently 15 years old.
The ratio of Maggie's current age to Steven's current age is M/S = 10/15 = 2/3 which turns into 2:3
In 10 years, Maggie will be M+10 = 10+10 = 20 and Steven will be S+10 = 15+10 = 25
The ratio of their ages now is (M+10)/(S+10) = 20/25 = 4/5 leading to the ratio 4:5
This confirms our answers.