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# Mary is 24 years old. She is twice as old as Ann when Mary was as old as Ann is Now. How old is Ann?

#8
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Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

I'll admit, rosala....this one IS a "stumper."  I think the verbiage in the problem is the confusing thing....until Alan and Melody explained it...I didn't see it, either.

Using what they said......

Mary's age now = 24

So...some years ago (let's call this "x") Mary was as old as Ann is now.  And let's call Ann's current age "A" Therefore:

24 - x  = A  .......Let's call this "Equation 1"

And, as Alan has noted, x years ago, Ann's age was just, A - x.

Now here's the tricky part............"Mary.... is twice as old as Ann was"......

Let's stop right there........"is twice as old as Ann was" means that Ann's age at the time, (A - x), times 2 must equal  Mary's age now - (24)  !!!

OR, equation-wise......

(A - x) * 2 = 24     ........divide by 2 on both sides......

(A - x ) = 12     .........add x to both sides.......

A = 12 + x    Let's call this "Equation 2"

And remember, from Equation 1, we have that 24 - x = A

Therefore Equation 1  must equal Equation 2 because A = A....so we have.....

24 - x = 12 + x       ......add x to both sides......

24 = 12 + 2x          ......subtract 12 from both sides.......

12 = 2x                   ......divide both sides by 2.....

x = 6

Therefore, since A = 12 +x, then 12 + 6 = 18 and that's Ann's current age!!!

P.S.....The complex wording of this problem makes it almost indecipherable. I might have stated it thusly:

Mary is 24.  Ann is younger. When Mary was Ann's current age, Ann was half of Mary's current age. How old is Ann??

Yeah...I think that works...!!!   Jun 28, 2014

#1
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Have u checked or written the question correctly becoz i dont know why i feel theres something missing or u havent written it correctly! It seems quite confusing becoz of  the way uve written it !But still im trying to solve it but its again and again confusing me!Please check if everything is right in the question! Jun 28, 2014
#2
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Have u checked or written the question correctly becoz i dont know why i feel theres something missing or u havent written it correctly! It seems quite confusing becoz of  the way uve written it !But still im trying to solve it but its again and again confusing me!Please check if everything is right in the question! Jun 28, 2014
#3
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Oops!sorry that was a mistake ! Jun 28, 2014
#4
+8

I think the question is:

Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

Mary = 24

x years ago:   Mary - x = Ann  so 24 - x = Ann

Also:   Mary = 2(Ann - x)

So:   24 = 2(24 - x - x)

:   24 = 48 - 4x

:   x = 6

Ann = 24 - x = 24 - 6, so Ann = 18

Jun 28, 2014
#5
+8

Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

Y years ago Ann was half 24yrs = 12years SO

Ann-Y=12 so Ann=12+Y  (1)

24-Y=Ann's age now  (2)      (Ann is the same age now as Mary was Y years ago)

24-Y=12+Y       (2)=(1)

12=2Y

Y=6

Ann=12+6=18 years.

Alan's way may be more elegant but this is just how I got my head around it.  Both are correct. I have added this one to the sticky topic "Puzzles"

Jun 28, 2014
#6
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I cant understand the question now also after your simplification Alan, i dont know why!this question is confusing me very much ! pls can amyone simplify it more like into separate sentences so i can get what is it!and as i understand the question im sure ill easily understand your excellent answers as well !so pls can u make me understand the question! Jun 28, 2014
#7
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Mary is now 24 years old.

Ann is now A years old.

When Mary was A years old, Ann was B years old.

Mary is now 2*B years old.

How old is Ann now?

Jun 28, 2014
#8
+8

Mary is 24.  She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?

I'll admit, rosala....this one IS a "stumper."  I think the verbiage in the problem is the confusing thing....until Alan and Melody explained it...I didn't see it, either.

Using what they said......

Mary's age now = 24

So...some years ago (let's call this "x") Mary was as old as Ann is now.  And let's call Ann's current age "A" Therefore:

24 - x  = A  .......Let's call this "Equation 1"

And, as Alan has noted, x years ago, Ann's age was just, A - x.

Now here's the tricky part............"Mary.... is twice as old as Ann was"......

Let's stop right there........"is twice as old as Ann was" means that Ann's age at the time, (A - x), times 2 must equal  Mary's age now - (24)  !!!

OR, equation-wise......

(A - x) * 2 = 24     ........divide by 2 on both sides......

(A - x ) = 12     .........add x to both sides.......

A = 12 + x    Let's call this "Equation 2"

And remember, from Equation 1, we have that 24 - x = A

Therefore Equation 1  must equal Equation 2 because A = A....so we have.....

24 - x = 12 + x       ......add x to both sides......

24 = 12 + 2x          ......subtract 12 from both sides.......

12 = 2x                   ......divide both sides by 2.....

x = 6

Therefore, since A = 12 +x, then 12 + 6 = 18 and that's Ann's current age!!!

P.S.....The complex wording of this problem makes it almost indecipherable. I might have stated it thusly:

Mary is 24.  Ann is younger. When Mary was Ann's current age, Ann was half of Mary's current age. How old is Ann??

Yeah...I think that works...!!!   CPhill Jun 28, 2014
#9
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Thank u very much Alan and CPhill!after ur boths simplification i see that the question was not that difficult also  as i thought !thumbs up and points from me for all ur answers to this question Alan , CPhill and Melody ! Jun 29, 2014
#10
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Thank you rosala :-)

Jun 29, 2014
#11
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Your Welcome Melody! Jun 29, 2014
#12
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Ann is 12 because twenty-four divided by two is twelve!😛

Mar 30, 2015
#13
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Dec 2, 2015
#14
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When Marry 18,

Ann would be what?

9 (half of it) --> 9 years diff

That is so wrong..

How about 16 (Marry),and 8 (Ann) --> 8 years diff.

Now 24 y.o. Marry and 16 y.o. Ann..

Still 8 years diff..

Go figure

Jan 25, 2017