Q&A - PSLE Math

[tianzhu]

2DMommy:

Thanks TianZhu !


I have another question, is there a easy way to solve this question?

A bag of oranges were shared among some girls. If each girl received 5 oranges, there would be 1 extra orange. If each girl received 6 oranges, there would be 4 oranges short.
a) How many oranges were therein the bag?
b) How many girls were sharing the oranges?

Thks !

Hi

You're welcome.

You can solve it in two ways

One way is to use a tabulated list (Systematic listing).

The other way is;

Gap ----- (1+4) ------- 5 oranges

Difference in oranges per girl------- (6-5) ------ 1 orange

Number of girls ------- 5/1 -------5

Number of oranges ------- (5*5) + 1 ------ 26
\t
Best wishes

[pixiedust]

TianZhu, the apples and oranges question is killing me. I keep assuming the number must be multiples of 7 and 9.... :stupid: Will wait for solution.


Re: oranges and girls : wow! I like your elegant solution !

[atutor2001]

pixiedust:

...Will wait for solution...

Simply :

Let the number of GROUPs of \"7 apples\" be U
Let the number of GROUPs of \"9 oranges\" be V

1 group of apple costs $4 so cost of all apples is $4U
1 group of orange costs $11 so cost of all oranges is $11V
So 4V + 11V = 999

Total number of apples is 7U (there are 7 apples in each group)
Total number of oranges is 9V (there are 9 oranges in each group)
So 7U + 9V = 1000

To find U & V we can draw model or use simultaneous.

[small]

Different way to solve the question.


http://farm6.static.flickr.com/5020/5456292860_49335b2630_z.jpg\">

[atutor2001]

small:

Different way to solve the question.


http://farm6.static.flickr.com/5020/5456292860_49335b2630_z.jpg\">

If the question is :

A bag of oranges were shared among some girls. If each girl received 5 oranges, there would be 4 extra oranges. If each girl received 6 oranges, there would be 4 oranges short.

What should I do, using the same method?

[tianzhu]

anneshirleygilbert:

I did it the Guess and Check method and got the answer after 10 guesses!!! Doubt students sitting in PSLE would have the luxury of time to do 10 guesses.

My answer is 343 apples and 657 oranges; but I'm curious and eager to learn your method.

Hi

Hope this helps.

First I’d like to share the thought process for this solution.

A student should be able to recognize that the number of oranges is a multiple of 9 and the number of apples is a multiple of 7.

I started with a group of 100 for ease of calculation as it’s not too difficult to get 72 oranges and 28 apples to form a group of 100 fruits.

Next multiply by 10 to get 1000 fruits.

Work in group of 63 for an increase/decrease of oranges and apples --- for balancing.

Best wishes

http://farm6.static.flickr.com/5052/5456348000_75a99120c9_b.jpg\">

[small]

atutor2001:

If the question is :

A bag of oranges were shared among some girls. If each girl received 5 oranges, there would be 4 extra oranges. If each girl received 6 oranges, there would be 4 oranges short.

What should I do, using the same method?

Hope this helps.

a)

Multiple of 5 + 4 : 19, 24, 29, 34, 39, 44, 49, 54, 59\t.....
Multiple of 6 - 4 : 20, 26, 32, 38, 44, 50, 56, 62...

There were 44 oranges in the bags.\t\t\t\t\t\t\t\t\t\t\t

b) \t If each girl received 5 oranges, there would be 4 extra oranges.\t\t\t\t\t

\t5 Units + 4 = 44
\t5 Units = 40
\t1Unit = 8

\t8 girls were sharing the oranges.

[small]

tianzhu:

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5052/5456348000_75a99120c9_b.jpg\">

Hi Tianzhu,

Like this method, thanks for sharing the idea. :celebrate:

[atutor2001]

small:

atutor2001:

If the question is :

A bag of oranges were shared among some girls. If each girl received 5 oranges, there would be 4 extra oranges. If each girl received 6 oranges, there would be 4 oranges short.

What should I do, using the same method?

Hope this helps.

a)

Multiple of 5 + 4 : 19, 24, 29, 34, 39, 44, 49, 54, 59\t.....
Multiple of 6 - 4 : 20, 26, 32, 38, 44, 50, 56, 62...

There were 44 oranges in the bags.\t\t\t\t\t\t\t\t\t\t\t

b) \t If each girl received 5 oranges, there would be 4 extra oranges.\t\t\t\t\t

\t5 Units + 4 = 44
\t5 Units = 40
\t1Unit = 8

\t8 girls were sharing the oranges.

Hi small

Multiple of 5 + 4 : 9, 14....

Multiple of 6 - 4 : 2, 8, 14, ....

Actually the first common number is 14, why is 14 not the number of oranges? Thanks

[small]

Hi atutor2001,


You are right too, I overlooked this, still have long long way to learn it. :oops:


I think normally the setter will specify the range of oranges for the question. If not, both 14 and 41 are considered correct..