SOLUTION: Lina is twice as old as Ana while Laarni is 24 years younger than Lina.If half of Lina's age six years ago was three less than one-half the sum of Ana's age in four years and Laarn

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Question 682081: Lina is twice as old as Ana while Laarni is 24 years younger than Lina.If half of Lina's age six years ago was three less than one-half the sum of Ana's age in four years and Laarni's present age,find the ages of each.
Found 2 solutions by JBarnum, MathTherapy:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
I love age word problems
anyway
i always use first letter of names so its not so confusing
well unless they double i will use another letter
L=Lina
A=Ana
I=Laarni
L=2A
I=L-24
(wow this is a horrible question please smack the creator of this question)
%28L-6%29%2F2=%28%28%28A-4%29%2BI%29%2F2%29-3 woowee that is a mind buster but im sure i got it right
ok so if L=2A substitute (L) in I=L-24 which is I=2A-24
now you have what (L) and (I) equal so replace them in the long equation
%28highlight%28L%29-6%29%2F2=%28%28%28A-4%29%2Bhighlight%28I%29%29%2F2%29-3
%28highlight%282A%29-6%29%2F2=%28%28%28A-4%29%2Bhighlight%282A-24%29%29%2F2%29-3 divide by 2 an left side and add like terms on right side
%28A-3%29=%28%283A-28%29%2F2%29-3 add 3 to each side
A=%283A-28%29%2F2 multiply by 2
2A=3A-28 subtract 2A and add 28 to both sides
highlight%2828=A%29 now that you have what (A) equals you can solve for the others
L=2A
L=2%2828%29
highlight%28L=56%29
I=L-24
I=56-24
highlight%28I=32%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Lina is twice as old as Ana while Laarni is 24 years younger than Lina.If half of Lina's age six years ago was three less than one-half the sum of Ana's age in four years and Laarni's present age,find the ages of each.

Let Ana’s current age be A
Then Lina’s is 2A
Laarni is 2A – 24
½(2A – 6) = ½(A + 4 + 2A – 24) - 3
%282A+-+6%29%2F2+=+%283A+-+20%29%2F2+-+3
2A – 6 = 3A – 20 – 6 ------ Multiplying by LCD, 2
2A – 3A = - 26 + 6
- A = - 20
A, or Ana’s current age = %28-+20%29%2F-+1, or highlight_green%2820%29

Lina’s is 2(20), or highlight_green%2840%29

Laarni’s is 2(20) – 24, or 40 – 24, or highlight_green%2816%29

You should be able to do the check!!!

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