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I am not sure on what should be the quick way of approach to solve these kind of questions. As we grow, we can think of other possible ways to solve the same problem. Many genius can solve the algebra questions orally. I am not sure how can they solve. But, If I need to solve the equations then certainly I can't solve it orally. Am I correct on it? Does somebody has a more quicker way to solve the question below - using arithmetic or other concept to solve this question orally?

Problem - Given that sum of Abi and Iris age is 42 years. 11 years ago, Abi was three times as old as Iris. how old Abi will be in 2 years?

This is my approach -- Please tell me how you would have solved such questions.
Also, how much time will you take to solve this type of question.

make two equations - considering the present age always -

a + i = 42

a-11 = 3 ( i - 11)

Now, solve for them -

a = 26 and i = 16.


The answer is a +2 i.e. 28 years.
dexterous
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  • Nice question, just note that it is not really obvious what counts as "using algebra". Usually, while an approach may be more intuitive, the algebra is still there, it has just been made to wear a fake beard and sunglasses. – Klaus Draeger Oct 06 '14 at 13:14

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Solving problems such as these (and far more complicated than this, too) without algebra is encouraged in the Singapore system. Before I started teaching my son, I would've immediately reached for algebra, but now simple arithmetic and model drawing are my weapons of choice.

$11$ years ago, the sum of their ages would've been $42-2 \times 11 = 42 - 22 = 20$.

Since Ari was $3$ times as old as Iris, think of the sum of their ages as $3+1 = 4$ parts. $4$ parts $= 20$ so $1$ part = $5$ years.

Therefore Iris was $5$ and Ari was $3 \times 5 = 15$ then, making Ari's present age $15 + 11 = 26$ and her age in $2$ years hence $26+2 = 28$ years.

Deepak
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  • As to your question about how much time I took, I did the problem mentally the moment I saw it on my other device (a tablet), and took about 20 seconds to do it in my head. It took significantly more time for me to wake my laptop up, connect to the site and type out the solution, properly formatted, than I did to get the answer in the first place. – Deepak Oct 06 '14 at 12:02
  • It just went above my head. Do you know any links to understand the singapore maths? I didn't get any of your equation. – dexterous Oct 06 '14 at 12:49
  • Which part, exactly, went above your head? Let me guess which part(s) might be slightly tricky. The first part about the sum of their ages $11$ yrs ago being $22$ yrs less is simple when you consider that each of them is $11$ yrs younger. Another slightly tricky part is the $4$ parts = $20$ yrs thing. It might help to represent Iris' age $11$ years ago as a single block, which would make Ari's age $3$ blocks. The sum of their ages is $4$ blocks, which is $20$ yrs. You can now figure out what a single block is, and the rest should be obvious. Primary school kids here start with block drawing. – Deepak Oct 06 '14 at 13:10
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    BTW, this is a very simple problem by Singapore Primary School standards. I can acquaint you with some problems that become truly fiendish when you try to solve them without the familiar crutch of algebra. Word problems involving tanks of different volumes filling and draining at different rates can be especially tough when working purely "conceptually" without just writing out the equations and blasting through them. – Deepak Oct 06 '14 at 13:15
  • Do you suggest to stick with traditional algebra method only? Do you say that model way may become difficult as the problem level becomes tougher. – dexterous Oct 06 '14 at 13:32
  • Personally, I find that the model method is more natural for the really easy problems (this is a little on the borderline, but still fairly tractable). When the problems get tougher, the model method seems far more unnatural than just using algebra. So I have some reservations about the methods taught in Singapore, where the students are not officially "allowed" to use algebra until about age 11 or so. – Deepak Oct 06 '14 at 13:34