SOLUTION: Paul is twice as old as Timothy this year. if their combined age is 54 years, what will be their combined age when Timothy is as old as Paul is this year?

Let Paul be P years old this year and Timothy be T years old this year. 

P = 2T

P+T = 54

Substitute 2T for P in P+T = 54

2T+T = 54
  3T = 54
   T = 18

Timothy is 18.

Substitute 18 for T in P = 2T

P = 2(18)

P = 36

Paul is 36.

Timothy is 18 and Paul is 36.  It will take another 18 years for Timothy to be
36, which is how old Paul is this year.  But in 18 years Paul will be 54.  So
their combined age then will be 54+36=90. 

Edwin