how about a strategy instead of a solution:
let a = the age of alice at present and let b = the age of her brother at present
what is an equation for the relationship of their present ages (hint: in words it is "alice is 4 times her brother's current age")?
what about 10 years from now: how old will alice be (hint: 10 years older than she is now, which now is "a")? and how old will her brother be (hint: 10 years more than "b")?
so what is the equation for the relationship of their ages 10 years from now (hint: in words it is "alice will be twice as old as her brother")?
now, we 2 equations (the 2 above) and two unknowns ("a" and "b"). can you solve them?