SOLUTION: Maria is 36 years old. Maria was twice as old as Adrian was when Maria was as old as Adrian is now. How old is Adrian?

Question 1166222: Maria is 36 years old. Maria was twice as old as Adrian was when Maria was as old as Adrian is now. How old is Adrian?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
m = maria's age now.
a = adrian's age now.

maria is 36 years old now, so the formula for that is m = 36.

maria was twice as old as adrian was when maria was as old as adrian is now.
let x = the number of years ago when this occurred.

if you let x equal the number of years ago when maria was as old as adrian is now, then the formula for that is m - x = a

the statement says that maria was twice as old as adrian was when maria was as old as adrian is now.
the formula for that is m - x = 2 * (a - x)
since (m-x) = a, then replace a in this formula to get:
m - x = 2 * (m - x - x)
combine like terms to get:
m - x = 2 * (m - 2x)
simplify to get m - x = 2m - 4x
subtract m from both sides of the equation and add 4x to both sides of the equation to get 4x - x = 2m - m
combine like terms to get 3x = m

since m = 36, then you get:
3x = 36
solve for x to get:
x = 12

since m - 14 = a, then we also know that a is equal to 24.

your original formulas were:
m = 36
m - x = a
m - x = 2 * (a - x)

when m = 36 and x = 12, the formulas become:
m = 36 stays the same
m - x = a becomes 36 - 12 = 24 which becomes 24 = 24 which is true.
m - x = 2 * (a - x) becomes 36 - 12 = 2 * (24 - 12) which becomes 24 = 24 which is also true.

the values of m = 36 and x = 12 and a = 24 are good.

your solution is that adrian is 24 years old.

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