# Question

Some children were at a party. If 45 boys left the party, the ratio of the number of boys to the number of girls would become 5:3

If 38 girls left the party, the ratio of the number of boys to the number of girls became 2:1

How many children were at the party?

Some children were at a party. If 45 boys left the party, the ratio of the number of boys to the number of girls would become 5:3

In the end, Boy 5 units and Girl 3 units  –> At first, Boy 5 units + 45 and Girl 3 unit

If 38 girls left the party, the ratio of the number of boys to the number of girls became 2:1

At first, Boy 5 units + 45 and Girl 3 unit –> In the end, Boy 5 units + 45 and Girl 3 units – 38

5u + 45 = 2p

3u – 38 = 1p –> 6u – 76 = 2p

5u + 45 = 6u – 76

1u = 76 + 45 = 121

8u + 45 = 1013

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Model above is essentially same as Alfretztay and Dazzlego (units and parts method). I tried to draw model for testing because I recalled a previous question (link here)  that parent (or child) prefers model drawing . Then, it leads me to post the below for discussion.

What I would want to say is this: This model may seem easy in this case. But there are cases where setter did not consider different methods (including model) but only thought about using “units and parts method”. For example, instead of 2:1 in the last ratio, it is 3:2 or 7:3. We can all imagine the hassle to draw “LCM” models to equate the two. This is when “units and parts method” prevails.

It then becomes a good opportunity to let the child understand the rationale and the need to learn and practice more methods, especially if one gets too comfortable with a particular method and is reluctant to learn, try and do other methods. I used to grab such opportunities to explain the rationale and need for DC to do left, right and centre just for one question like that. Yes, there was resistance from DC thinking it is a waste of time. But I force it anyway. After all, the purpose of school is keep on learning.

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Model above is essentially same as Alfretztay and Dazzlego (units and parts method). I tried to draw model for testing because I recalled a previous question (link here)  that parent (or child) prefers model drawing . Then, it leads me to post the below for discussion.

What I would want to say is this: This model may seem easy in this case. But there are cases where setter did not consider different methods (including model) but only thought about using “units and parts method”. For example, instead of 2:1 in the last ratio, it is 3:2 or 7:3. We can all imagine the hassle to draw “LCM” models to equate the two. This is when “units and parts method” prevails.

It then becomes a good opportunity to let the child understand the rationale and the need to learn and practice more methods, especially if one gets too comfortable with a particular method and is reluctant to learn, try and do other methods. I used to grab such opportunities to explain the rationale and need for DC to do left, right and centre just for one question like that. Yes, there was resistance from DC thinking it is a waste of time. But I force it anyway. After all, the purpose of school is keep on learning.

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Just my opinion here.

Models as a teaching tool is great to visualize single variable algera. By psle, the student needs to get comfortable with units and parts. Coz drawng models is too time consuming for exams.

the student needs to get comfortable with units and parts

Agreed. Knowledge in solving with units and parts is necessary because not all problems can be conveniently reduced to single variable like in this question.

Coz drawng models is too time consuming for exams

Unfortunately, for some students (eg. my daughter), this visual aid determines whether she can solve the problem or not. So at the beginning of P6, she was trained to draw model quickly, neatly and clearly without using model ruler. Also, even with units and parts question, it is still possible to draw model to help visualise the problem.

Take this question as example, I would draw a units and parts model (in free hand) like so…

Information in black ink are those transferred from the question, while those in red are deduced from the before model.

Of course, don’t use a red pen during exam!  😆

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Allow me to present an alternative model….

I admit this is not conventional…most schools don’t teach drawing model this way. The conventional way of solving this problem is by units and parts, presented by Alfretztay and Dazzlego.

This model, on the other hand, eliminates the need to deal with units and parts, and some children might just appreciate it.

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Method 1 :
(number of boys – 45)/number of girls = 5/3
3 x number of boys – 135 ——- 5 x number of girls
3 x number of boys ——- 5 x number of girls + 135
number of boys/number of girls – 38) = 2/1
1 x number of boys ——- 2 x number of girls – 76
3 x number of boys ——- 6 x number of girls – 228
6 x number of girls – 228 ——- 5 x number of girls + 135
number of girls ——- 135 + 228 = 363
number of boys ——- 2 x 363 – 76 = 650
650 + 363 = 1013

Method 2 :
Scenario 1 : If 45 boys left the party,
boys : girls
5u : 3u

Scenario 2 : If 38 girls left the party,
boys : girls
2p : 1p

5u + 45 ——- 2p
3u ——- 1p + 38
5u + 45 ——- (3u – 38) x 2 = 6u – 76
6u – 5u = 1u ——- 45 + 76 = 121
8u ——- 8 x 121 = 968
968 + 45 = 1013

Ans : 1013 children.

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