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[Maths Monster]

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[Vanilla Cake]

Herbie:

Thanks VC and Dharma Can help with the qn below?


There were some chairs in a school hall. 1/2 of the chairs were placed in short rows while 2/5 of the chairs were placed in long rows. The rest of th chairs were stacked at the back of the hall.

There were 15 short rows and long rows. If each short row contained 7 chairs less tha each kong rows, how many chairs were there in the wall altogether?

Tx

Hi Herbie,
May I know the source of this question?

Maths Monster:

Can anyone can solve this without using guess and check method?

P6 SA1 2009 Paper2 Q14

Audrey and Belle has some money each. If Audrey spends $18 and Belle spends $24 each day, Audrey will have $25 left when Belle has spend all her money. If Audrey spends $13 and Belle spends $30 each day, Audrey will have $139 left when Belle has spend all her money. How much money do they have altogether?

[Ans: 655]

Hi Maths Monster,
Thanks for posting this interesting 4-mark question from Nanyang P6 SA1 2009 paper 2 Q14 and let's look forward for creative solutions from readers in this forum plus our dearest Mathsguru to provide her model solution.
For the reference of readers, this question had been discussed in other forum and blog.

http://psle2010a.blogspot.com/2010/03/14.html
http://www.onsponge.com/forum/35-thinkingmathonsponge/2528-p6-maths.html
http://www.onsponge.com/forum/35-thinkingmathonsponge/1917-p6-maths-2009-nanyang-sa1-paper-2.html

[tisha]

Is it possible to solve these without algebra? These are P5 Questions from past year exam papers for SA1.

I believe algebra is only taught in P6, so just curious how come these questions can be asked for SA1 of P5 :?

Ken and Patrick had $625 at first. After buying some books, the amount of money Ken has left is 4 times the amount of money he spent and the amount of money Patrick has left is 5 times the amount of money he spent. Find the amount of money Patrick had at first if they have a total of $510 left.


There are 85 plates of chicken rice for 80 people. Each adult eats 2 plates of chicken rice and every 3 children share 1 plate of chicken rice. Find the number of adults and children respectively.

[Herbie]

Hi VC,


Source SJIJ P6 2010 CA 1 Paper

[Daddy]

Hi Maths Monster,


I have question to ask you. Thanks

1. A worker managed to complete 2/5 of his work on the first day and 3/4 of the remainder on second day. How much work was completed at the end of second day?


Daddy.
Thanks alls.

[CoffeeCat]

tisha:

Is it possible to solve these without algebra? These are P5 Questions from past year exam papers for SA1.

I believe algebra is only taught in P6, so just curious how come these questions can be asked for SA1 of P5 :?

Ken and Patrick had $625 at first. After buying some books, the amount of money Ken has left is 4 times the amount of money he spent and the amount of money Patrick has left is 5 times the amount of money he spent. Find the amount of money Patrick had at first if they have a total of $510 left.


There are 85 plates of chicken rice for 80 people. Each adult eats 2 plates of chicken rice and every 3 children share 1 plate of chicken rice. Find the number of adults and children respectively.

For qns 2. One common non-algebra way to solve such algebraical questions is to use this heuristic called \"make an assumption\".
First assume there are 80 adults. Then these 80 adults will eat 160 plates of rice.
Now we must try to find the number of children.
Notice that if we interchange 3 adults for 3 children, there will be a decrease in (2*3 -1) = 5 plates of rice from the total.
(if you are not convinced you can try 77 adults, 75 adults to see the pattern)
For every group of interchange of 3 adults for 3 children, we are 5 plates nearer the true total of 85. therefore, the number of children is 3*(160-85)*5 =45.

[CoffeeCat]

Daddy:

Hi Maths Monster,


I have question to ask you. Thanks

1. A worker managed to complete 2/5 of his work on the first day and 3/4 of the remainder on second day. How much work was completed at the end of second day?


Daddy.
Thanks alls.

3/4 of the remainder of job = 3/4 * (1- 2/5) = 9/20 of work
amt of work completed at end of second day = 2/5 + 9/20 = 8/20 + 9/20 = 17/20

[small]

Hi tisha,


Hope this clear enough.


Question:
Ken and Patrick had $625 at first. After buying some books, the amount of money Ken has left is 4 times the amount of money he spent and the amount of money Patrick has left is 5 times the amount of money he spent. Find the amount of money Patrick had at first if they have a total of $510 left

Total of $510 left -----> 4 units of Ken + 5 units of Patirck = 510 ---------------> (1)

The amount they spent -----> 1 unit of Ken + 1 unit of patrick = (625-510) = 115
4 units of Ken + 4 units of patrick = 115 x 4 = 460
4 units of Ken + 4 units of patrick = 460 ---------------> (2)

By substitute (2) in (1):
460 + 1 unit of Patrick = 510
1 unit of Patrick = 50

Patrick had 6 units at first.
6 x 50 = 300

Patrick had $300 at first.

[CoffeeCat]

Herbie:

Thanks VC and Dharma Can help with the qn below?


There were some chairs in a school hall. 1/2 of the chairs were placed in short rows while 2/5 of the chairs were placed in long rows. The rest of th chairs were stacked at the back of the hall.

There were 15 short rows and long rows. If each short row contained 7 chairs less tha each kong rows, how many chairs were there in the wall altogether?

Tx

Is there an answer key for this?
At first based on this \"There were 15 short rows and long rows.\", I take it that there are a total of 15 rows altogether.
Unless I am mistaken, this interpretation though interesting, only secondary mo technique can yield the answer of 630. Otherwise guess-and-check will be much easier. Unless this is what the school intended to test upon.
So perhaps it would make sense if it was 15 short and 15 long rows.

[Herbie]

There were some chairs in a school hall. 1/2 of the chairs were placed in short rows while 2/5 of the chairs were placed in long rows. The rest of th chairs were stacked at the back of the hall.


There were 15 short rows and 8 long rows. If each short row contained 7 chairs less tha each kong rows, how many chairs were there in the wall altogether.

Sorry, there is a typo error. There shld be 8 long rows.