Polya step 1: analyse the problem: two variables (two amounts of money) and two equations derived from two statements. Simultaneous equations problem.
Polya step 2: strategy is to use two algebraic variables and then derive equations from the given statements.
If I have $a and my sister has $b (step 3---apply the algebraic strategy).
Derive system of equations from given statements:
If I give her $1 she will have $(b+1); so a-1=b+1, a=b+2.
If she gives me $1 I will have $(a+1) so a+1=2(b-1)=2b-2, a=2b-3.
Polya step 4: solve and check:
Therefore b+2=2b-3, 5=b; she has $5 and I have b+2=2b-3=$7.
Check:
I have $7, sis has $5.
(1) I give her $1: I have $6 she has $6, same as me.✔️
(2) She gives me $1: I have $8, she has $4. I have twice as much as she does.✔️