Think you can try guess and check method, by using the total number of pencils vs sum of guessed boys and girls and their corresponding number of pencils they have.

I dun want that solution. I know it can be done that way. And i also can solve it using simultaneous equations. I want a model method if possible. Thanks

Difference in pencils between girls and boys = 60 - 20 = 40 Total pencils = 40 x 35 = 1400 Total pencils if all are boys = 40 x 20 = 800 Difference = 1400 - 800 = 600 Number of girls = 600 / 40 = 15 Hence, number of boys = 40 - 15 = 25 Or, Total pencils if all are girls = 40 x 60 = 2400 Difference = 2400 - 1400 = 1000 Hence, number of boys = 1000 / 40 = 25 Good if someone provides a model technique, good to learn more

Mm.. Why are the number of girls 600 ÷ 40?

That's the difference in number of pencils between each girl and boy. So if divide by the difference, you will get the number of girls.

Oh. Ok thanks for the solution! Nice to learn something new

You're welcomed, I'm also learning :)

Or...

I think Jason Oon's method is good. Another way to think about this is: Since we know that the average number of pencils each pupil had was 35. That means we need to distribute the pencils from the girls to the boys: Therefore, the number of pencils given by 1 girl: the number of pencils received by 1 boy = 25 : 15 = 5 : 3. Obviously, the total number of pencils given by the girls = total number of pencils received by the boys. For that to happen, the number of girls : the number of boys = 3 : 5. Since there are 40 pupils in all, we know that 8 units of pupils represent 40 pupils, 1 unit of pupils = 5 students and so, the number of boys = 5 x 5 = 25.

Er..dun want algebra or guess and check..but thanks..

Nice..thanks Choy Ban Heng! Can't be any clearer man

Hi Travis Neo, I think a Model Method solution in this case will be too contrived. There are problems, like this one, that are best solved by supposition (as in Jason Oon's method), guess and check, or simply by using the concept of average and ratio. The mathematics syllabus does not restrict solution methods to the model method only. If you are helping your child, it will be best to encourage a variety of solution methods so that the child can develop a repertoire of problem solving strategies that he/she can call upon.

Eh wait a min..how did u derive the fact that number of pencils given by 1 girl : number of pencils received by 1 boy = 25: 15? Oh no..i am lost again

Because the average is 35, the girl's average is 60, so each girl needs to give up 25 pencils to reach 35, and each boy needs to get 15 more to reach 35.

Ah...ok!!

Hi Jason... Why 40 x 35 = 1400? How did that give total pencils?

Hi Julie, 35 is the number of pencils each pupil has on average. Since there is a total of 40 pupils, the total number of pencils is 40 pupils times 35 pencils per pupil, hence giving the total of 1400 pencils.

Oops... your right. . Thanks...

May I know what level Math this is?

P5

Which solution is the school taught method?

It depends..both Jason's and Choy's method and guess and check can be used

??????

First ask, "can there be an equal number of boys and girls?" (No, there should be more boys than girls. Why so?) Ask, " if you replace 1 girl by 1 boy, how many fewer pencils will there be?" (40 pencils) Ask, "how many boys and girls do you think there are?" (There are more than 20 boys, and less than 20 girls. What if there are 21 boys and 19 girls? What if there are 22 boys and 18 girls? ...) Allow students to figure out the answer in their own ways.

No. Pencils per head x head = total pencils. Similar to rectangular area Answer No of boys 25 no of girls 15

The area model is useful for solving problems involving averages.

You may draw two bars of different widths for boys and girls. The widths represent the numbers of boys and girls. The lengths represent the respective averages. Then the areas of the bars represent the respective numbers of pencils. In this way we have a 2D bar model drawing.

I don't get it man..the solution looks more puzzling than the question..lol

Travis Neo -- This method is helpful in some problems especially the problems on mixture, speed and distance, average... or the problem that contain multiplication between every two variables.. which is similar to the rectangle area concept (=widthx long)

D. Requires visualising parallel shifts of lines

Thank you so much.

The answer to this question is D

Solution made Visual :P

Thank you

Thanks teacher, it shows that the answer from the publisher is wrong. wahahaha

Some corrections to her model -- the $2 should not be part of the 50%. Correction to the working in the photo -- 50% (not 100%) represents 2+4+2. Hope she can continue from here...

Thanks teacher, it shows that the answer from the publisher is wrong. wahahaha