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I am new to Singapore mathematics. I could solve this question very easily using algebra. However, I feel that you get a good picture - conceptually when you try to solve questions using singapore mathematics. The variables x,y - algebra hide the deep understanding. Do you agree? Can you share me some right books - singapore mathematics -- links to start understanding singapore maths so that I can solve any complex problem without using algebra. Anyway, here is my question that I am trying to solve using singapore mathematics.

Present ages of Sameer and Anand are in the ratio of $5 : 4$ respectively. Three years hence, the ratio of their ages will become $11 : 9$ respectively. What is Anand's present age in years?

Henry
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dexterous
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  • Why don't we have a tag for Singapore Mathematics? I don't have the required points to create a tag for Singapore mathematics. – dexterous Oct 08 '14 at 09:30

2 Answers2

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$\overbrace{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline & & & & & & & & & & \hline\end{array}}^{\text{Sameer's age in 3 years}}$

$\overbrace{\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline & & & & & & & & \hline\end{array}}^{\text{Anand's age in 3 years}}$

We must remove the same amount of boxes (representing 3 years) so as to get a ratio of $5:4$. Removing one box should do it. So one box is $3$ years. Sameer is currently $30$; Anand is $24$.

paw88789
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  • I am not getting the logic of why not -- 3(block size) multiplied by 4 to get the present age? Why 3(block size) is multiplied by the new ratio - 10:8. I am saying because the new ratio 10:8 is after 3 years. So, it is the future ratio and not the present one. – dexterous Oct 08 '14 at 11:01
  • To get the 5:4 ratio in the blocks that I used, you have to use 10 blocks for Sameer and 8 blocks for Anand, as in the diagram. If you do 5 blocks to 4 blocks for current age, then you would add half a block each to get 5.5 to 4.5 for subsequent age, so in that scheme a block would be 6 years. Sameer's current age is $5\times 6=30$. I chose the representation that allowed the use of whole blocks throughout the problem. – paw88789 Oct 08 '14 at 12:19
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Let be $S$ and $A$ the current ages of Sameer and Anand and rephrase the words.

So, today $$\frac{S}{A}=\frac{5}{4}$$ In three years time from now, we shall have $$\frac{S+3}{A+3}=\frac{11}{9}$$

I am sure that you can take from here.

Claude Leibovici
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