How old is Ana?

Algebra Level 2

Marvin is 33 years old. Marvin is three times as old as Ana was when Marvin was as old as Ana is now. How old is Ana now?


Try some of my problems: Math Problems - Set 1 .


The answer is 22.

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1 solution

the phrase "Marvin is three times as old as Ana was..." means that the age of Marvin now is three times the age of Ana x x y e a r s years a g o ago

the phrase "when Marvin was as old as Ana is now" means the age of Marvin x x y e a r s years a g o ago is equal to the age of Ana now

let: M M be the age of Marvin now;

A A be the age of Ana now;

A x A-x be the age of Ana x x y e a r s years a g o ago ;

M x M-x be the age of Marvin x x y e a r s years a g o ago

M = 33 = 3 ( A x ) M=33=3(A-x)

33 = 3 ( A x ) 33=3(A-x)

11 = A x 11=A-x ---->(1)

M x = A M-x=A

33 x = A 33-x=A --->(2)

from (1), x = A 11 x=A-11

from (2), 33 A = x 33-A=x

since the difference of their ages is always equal, we equate x = x x=x ,

A 11 = 33 A A-11=33-A

A = 22 A=22

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