SOLUTION: together, Thabo and his sister are twenty four years old. Three years ago, Thabo was twice as old as his sister was then. how old are they now ?

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Question 1187540: together, Thabo and his sister are twenty four years old. Three years ago, Thabo was twice as old as his sister was then. how old are they now ?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let x = thabo's age now.
let y = his sister's age now.

you are given that x + y = 24
you are also given that (x - 3) = 2 * (y - 3)

simplify the second equation to get:
x - 3 = 2y - 6
add 3 to both sides of the second equation and subtract y from both sides of it to get:
x - 2y = 3

your two equations that need to be solved simultaneously are:

x + y = 24
x - 2y = 3

subtract the second equation from the first to get:
3y = 27
solve for y to get:
y = 9

note that x - x = 0
note also that y - (-2y) = y + 2y = 3y

since x + y = 24, then x must be equal to 15 because 15 + 9 = 24

confirm the solution is correct by replacing x with 15 and y with 9 in the original equations.

x + y = 24 becomes 15 + 9 = 24 which becomes 24 = 14 which is correct.
(x - 3) = 2 * (y - 3) becomes (15 - 3) = 2 * (9 - 3) which becomes 12 = 12 which is also correct.

the solution is confirmed to be good.
the solution is that that thabo is cureently 15 years old and his sister is 9.



Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
together, Thabo and his sister are twenty four years old.
Three years ago, Thabo was twice as old as his sister was then.
how old are they now ?
~~~~~~~~~~~~ 

Three years ago, the sum of their ages was, OBVIOUSLY, 24 - 3 - 3 = 18 years,

AND Thabo was twice as old as his sister.


At this point, it is OBVIOUS, that three years ago Thabo was 12 years old, and the sister was 6 years old.


Hence, now Thabo is 12+3 = 15 years old, while his sister is 6+3 = 9 years old.    ANSWER

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So,  the problem is easily solved  MENTALLY,  using logical reasoning.



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