Question 1182774: Harry is 3 times as old as Louise was when Harry was as old as Louise is now. When Louise is as old as Harry is now, they will be 28 together. How old is Harry and Louise now?
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850)   (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
Harry is 3 times as old as Louise was when Harry was as old as Louise is now.
When Louise is as old as Harry is now, they will be 28 together. How old is Harry and Louise now?
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The solution by @MathLover1 is TOTALLY WRONG and INADEQUATE.
Simply ignore her post, for your safety.
The correct solution is below.
Let H be Harry's age;
let L be Louise's age.
From the condition, it is clear that Harry is older than Louise.
Let's transform / (translate) the problems statements into Math equations.
(1) When Harry was as old as Louise is now ? - - - It was (H-L) years ago.
At that time, Louise age was (L - (H-L)) years old.
So, we write our first equation
H = 3*(L - (H-L).
It is the same as
H = 3*(2L - H),
or
H + 3H = 6L, or 4H = 6L, or 2H = 3L (1)
(2) When Louise will be as old as Harry is now ? - - - It will happen in (H-L) years from now.
So, we write our second equation
L + (H-L) + (H + (H-L)) = 28.
It is the same as
3H - L = 28. (2)
(3) Thus we have the system of 2 equations in 2 unknowns
2H - 3L = 0, (1)
3H - L = 28. (2)
Multiply equation (2) by 3 (both sides); then subtract equation (1) from it. You will get
9H - 2H = 28*3, it implies 7H = 84; hence H = 84/7 = 12.
Then from equation (1), 3L = 2*12 = 24; hence, L = 24/3 = 8.
ANSWER. Harry is 12 years old; Louise is 8 years old.
CHECK. Check it on your own that all the problem's conditions are satisfied.
Solved.
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It is a typical twisted age problem.
There is a bunch of lessons on age word problems
- Age problems and their solutions
- HOW TO algebreze and to solve age problems?
- A fresh formulation of a traditional age problem
- Really intricate age word problems (*)
- Selected age word problems from the archive
- Age problems for mental solution
- Age problem for three participants
- Miscellaneous age problems
in this site.
Read them and become an expert in solving age problems.
To see other solved age problem, similar to this twisted one, look into the lesson marked (*) in the list.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Age word problems".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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Do not forget to post your "THANKS" to me for my teaching.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Harry is 3 times as old as Louise was when Harry was as old as Louise is now. When Louise is as old as Harry is now, they will be 28 together. How old is Harry and Louise now?
That woman ABSOLUTELY has no clue. Thus, her answer is SHEER RUBBISH, so don't even look at her setup and solution.
Let Harry's and Louise's ages be H and L, respectively
It's absolutely essential to determine who's older. From the reading, it's obvious that Harry is older.
With Harry being older the difference in their ages is H - L
So, H - L years ago, Harry was L years-old
And, H - L years ago, Louise was L - (H - L), or 2L - H years-old
Given that Harry is 3 times as old as Louise was when Harry was as old as Louise is now, we get:
H = 3(2L - H)
H = 6L - 3H
4H = 6L___2H = 3L ----- eq (i)
When Louise is as old as Harry is now, Louise will be H years-old
And, at that time, Harry will be H + H - L = 2H - L
Given that, when Louise is as old as Harry is now, their ages will sum to 28, we have:
H + 2H - L = 28
3H - L = 28
3H - 28 = L ----- eq (ii)
2H = 3(3H - 28) ------ Substituting 3H - 28 for L in eq (i)
2H = 9H - 84
2H - 9H = - 84
- 7H = - 84
Harry's age, or 
2(12) = 3L ------ Substituting 12 for H in eq (i)
Louise, or 
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