SOLUTION: The combined age of two people is 91. Person A is twice as old as person B was when Person A was as old as Person B is now. How old is each person?

The combined age of two people is 91. Person A is twice as old as person
B was when Person A was as old as Person B is now. How old is each person?

>>...The combined age of two people is 91...<<

Translation into algebra:  A + B = 91

>>...Person A is twice as old as person B was when Person A was as old as
Person B is now...<<

Do a little bit of rewording in terms of "X years ago", and make
these two new sentences from it:

>>...Person A is twice as old as person B was X years ago...<<
>>...X years ago was when Person A was as old as Person B is now...<<

Taking the first new sentence:
 >>...Person A is twice as old as person B was X years ago...<<

X years ago, B wsa B-X, so

A = 2(B-X)

Taking the second :

>>...X years ago Person A was as old as Person B is now...<<

X years ago, A was A-X.  So 

A-X = B

So we have three equations and 3 unknowns:

A + B = 91
A = 2(B-X)
A-X = B

Can you solve that system of equations?  If not post again.

Answer: A = 52, B = 39, X = 13

Checking:

Their combined age is 91.  52+39 = 91.  That checks
>>...Person A is twice as old as person B was X years ago...<<
13 years ago B was 39-13 or 26, and A is 52 which is twice that.
That checks.
>>...X years ago Person A was as old as Person B is now...<<
13 years ago Person A was 52-13 or 39, and that's how old Person B
is now, so that checks.

Edwin
AnlytcPhil@aol.com