>>Mary is twice as old as Ann was when Mary was as old as Ann now is.

Ann is 57. Mary is how old?<<

Let M = Mary's age now

Let x = the number of years ago we are talking about.

Mary's age now = M

Ann's age now = 57

Mary's age then = M-x

Ann's age then = 57-x

>>...Mary [now] is twice as old as Ann was [then]...<<

Translation:   M = 2(57-x)

>>...Mary [then] was as old as Ann now is...<<

Translation: M-x = 57

So we have this system of equations:

               M = 2(57-x)

             M-x = 57

Solve the second equation for x

               x = M - 57

Substitute M-57 for x in the first equation

               M = 2[57-(M-57)]

               M = 2(57-M+57)

               M = 2(114-M)

               M = 228 - 2M

              3M = 228

               M = 228/3 = 76

That's the answer, Mary is now 76.

To check solve for x

         x = M - 57 = 76 - 57 = 19 years ago

           Mary's age now = M = 76

                Ann's age now = 57

Mary's age then = M-x = 76-19 = 57

Ann's age then = 57-x = 57-19 = 38

So back when Mary was 57, Ann was 38, and Mary, now 76, is

indeed twice Ann's age back then, 38.

Edwin 

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