Q&A - PSLE Math

[Dharma]

Vanilla Cake:

Sam went shopping at a department store. He spent 1/5 of his money on a sofa set and $786 on a washing machine. Later, he spent 1/8 of his remaining amount on a dining table. If the amount of money left was $86.35 more than half of the amount he had at first, how much money did Sam have at first?


:?:

Hi Vanilla Cake,

Assume amt of money Sam had = 140u
7/8 of remainder = 70u + 86.35
8/8 of remainder = 80u + (86.35x8)/7

140u = 28u + $786 + 80u + 98.685
32u= 884.685
140u =3870.50

Sam had $3870.50 at first.

[Dharma]

These are 2 good qns on rates


1) A jigsaw puzzle can be fixed if A works alone for 6 hours followed by B working alone for 12 hours. Alternatively, the same jigsaw puzzle can also be fixed if A works alone for 8 hours followed by B working alone for 6 hours.If A works alone for 3 hours and hands over the job over to B, how long will it take B to complete fixing the jigsaw puzzle.

2)Tom started work on a job for 30 days. Jerry continued the job alone for another 5 days and finally they worked together for another 10 days to complete that job.For the same job, if Tom and Jerry work together, they can complete it in 20 days.Assuming Tom and Jerry each work at a constant rate throughout, how many days will Tom take to complete that job alone?

[Denise]

Mother has 2000 sweets. She gave all the sweets to the children.

On the 1st day, the children ate 1/2 of the sweets.
The children continue to eat 1/3, 1/4, 1/5 …1/2000 of the of the remainder of the sweets from the previous day.
How many sweets were left at last?

[Dharma]

Denise:

Mother has 2000 sweets. She gave all the sweets to the children.

On the 1st day, the children ate 1/2 of the sweets.
The children continue to eat 1/3, 1/4, 1/5 .........1/2000 of the of the remainder of the sweets from the previous day.
How many sweets were left at last?

http://www.postimage.org/

[N3SKiasu]

tianzhu:

Hi

Since you can get the answer through MD, it shows that you are probably on the right track.

Please post your MD, and I'll see if I can offer some help to simplify it.Do it, I am sure you'll gain from it.

Hi Tianzhu,
Thanks for your encouragement, I managed to put it onto words doc and paste onto picture mgr, but somehow the picture looks small. Are you able to advise how to enlarge it? Sound silly, so sorry, very poor at this, in fact my child helped me on this, I am grateful of you guys help.
http://www.postimage.org/

Pls feel free to amend if not right.
Thank you.

[N3SKiasu]

Dharma:

Sorry N3SKiasu,


I've added the calculations to show how 1u = 5 and 1p = 3

Just to need to add some comments to make it clear
No. of boys = 4u + 1 = 7p
No. of girls = 8p + 1 = 5u

You need to solve the 2 eqns to find 1u and 1p.

Hope it is clear now.

Thanks so much Mr Dharma for your explanation.
I am clearer now. Will try figure it out.
Thanks again.

[tianzhu]

Hi N3SKiasu


Your MD is correct.

Hope to see more of them in the future.

[tianzhu]

Dharma:

1) A jigsaw puzzle can be fixed if A works alone for 6 hours followed by B working alone for 12 hours. Alternatively, the same jigsaw puzzle can also be fixed if A works alone for 8 hours followed by B working alone for 6 hours.If A works alone for 3 hours and hands over the job over to B, how long will it take B to complete fixing the jigsaw puzzle.

2)Tom started work on a job for 30 days. Jerry continued the job alone for another 5 days and finally they worked together for another 10 days to complete that job.For the same job, if Tom and Jerry work together, they can complete it in 20 days.Assuming Tom and Jerry each work at a constant rate throughout, how many days will Tom take to complete that job alone?

I’ve seen comments in other blog about solutions posted by regular problem solvers. Readers want to see more alternative methods of arriving at a solution. Comments such as getting tired of eating chicken rice the whole week may have dampening effects to an enthusiastic problem solver, but it may be true to a certain extent.

So, I am not posting any solutions in this instance, but wish to check with Dharma whether the answers are correct.

Q1) 21 hours
Q2) 100 days

Questions on Rates and Averages may look innocently easy at first glance, but can be pretty challenging if you try them, especially under stressful examination environment.

I hope Dharma can share with us more interesting questions in the future.

[Dharma]

tianzhu:

Dharma:

1) A jigsaw puzzle can be fixed if A works alone for 6 hours followed by B working alone for 12 hours. Alternatively, the same jigsaw puzzle can also be fixed if A works alone for 8 hours followed by B working alone for 6 hours.If A works alone for 3 hours and hands over the job over to B, how long will it take B to complete fixing the jigsaw puzzle.

2)Tom started work on a job for 30 days. Jerry continued the job alone for another 5 days and finally they worked together for another 10 days to complete that job.For the same job, if Tom and Jerry work together, they can complete it in 20 days.Assuming Tom and Jerry each work at a constant rate throughout, how many days will Tom take to complete that job alone?

So, I am not posting any solutions in this instance, but wish to check with Dharma whether the answers are correct.

Q1) 21 hours
Q2) 100 days

Hi Tianzhu,

Both answers are correct

[tianzhu]

Dharma:

Both answers are correct

Hi Dharma
Thanks, anymore interesting questions on Rates and Averages?