Answer: John is 29 years old and Jane is 36 years old.
Explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[combine like terms]
[add both sides by 7]
[divide both sides by 2]
Now we know that y=36, we can plug that into either equations to find x.
[subtract both sides by 36]
This concludes that John is 29 years old and Jane is 36 years old.