Q&A - PSLE Math

[James Ang]

youngmum:

My boy got this problem. Can someone help me to solve this?


Monkey King had 2000 pears. He gave all the pears to some monkeys. On the first day, the monkeys ate half of the total number of pears. On the second day, they ate 1/3 of the remaining pears. On the third day, they ate 1/4 of the rest of the pears. They went on to eat the pears as 1/5,1/6,1/7,.....,1/2000 of the remainder of every previous day's pears. Find the number of pears left at the end.

Thanks. By the way, please explain clearly because i m a not so smart mum.

i calculated the remainder to be of this sequence,

1000, 666and2/3, 500, 400...
=> 2000/2, 2000/3, 2000/4, 2000/5....

the final remainder is 2000/2000 = 1 left.

Note: these pears must be magic pears because they can last for 2000 days (6years?) and also the monkeys can eat a fraction of one pear on some days.

[James Ang]

a school teacher asked me how to solve these two questions. Since these questions are common PSLE questions, I put them here for everyone's benefit to think about. If you want the answer, please let me know.


1. 80% of marbles are red marbles and 20% of them are blue marbles. 63 red marbles and 46 blue marbles are added. The red marbles now makes up 75% of marbles and blue marbles 25% of marbles. How many red marbles are there at first?

2. A van travelled from Town A to Town B at an average speed of 55km/h. A car started its journey from town B to A at 90 km/h at the same time the van started. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two town

[tianzhu]

Hi

Hope this helps.

http://farm3.static.flickr.com/2486/3943048915_0697cd38f6_o.jpg\">

[youngmum]

James Ang:

i calculated the remainder to be of this sequence,

1000, 666and2/3, 500, 400...
=> 2000/2, 2000/3, 2000/4, 2000/5....

the final remainder is 2000/2000 = 1 left.

Sorry James, I don't quite understand. I only know up to the 1000 part. :oops:

[James Ang]

youngmum:

James Ang:

i calculated the remainder to be of this sequence,

1000, 666and2/3, 500, 400...
=> 2000/2, 2000/3, 2000/4, 2000/5....

the final remainder is 2000/2000 = 1 left.

Sorry James, I don't quite understand. I only know up to the 1000 part. :oops:

1st remainder = 1/2 x 2000= 1000
2nd remainder = (1 - 1/3)x 1000 = 2/3 x 1000 = 666 and 2/3
3rd remainder = (1-1/4)x 666 and 2/3 = 3/4 x 666 and 2/3 = 500
4th remainder = (1-1/5) x 500 = 4/5 x 500 = 400
and so on...

so pattern is presented as below;
1000, 666and2/3, 500, 400...
=> 2000/2, 2000/3, 2000/4, 2000/5...... 2000/2000

the final remainder is 2000/2000 = 1 left.

[tianzhu]

Hi

Hope this helps.

http://farm3.static.flickr.com/2454/3943138731_61f5952233_o.jpg\">

[k1ndan]

1. Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio 3:2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of the a dictionary.



2. Marvin bought a box of fruits. 30% of the fruits are apples and the rest oranges. He realised that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found out that there were 52 more fruits in the box. How many fruits were there in the box at first?


3. Ann and Ben were given some money each. If Ann spent $25 each week and Ben spent $75 each week, Ann would still have $1350 left when Ben had sepnt all his money. If Ann spent $75 each week and Ben spent $25 each week, Ann would still have $150 left when Ben had sepnt all his money.

(a) How much money did Ann receive?
(b) How much money did Ben receive?

[enoawng]

The ratio of the number of stamps to number of marbles in Ali’s collection was 3:4. He gave aways 99 stamps and bought another 18 marbles. The ratio of the stamps to marbles became 3:7. How many stamps were left in Ali’s collection.


Appreciate any help. Thanks.

[James Ang]

enoawng:

The ratio of the number of stamps to number of marbles in Ali's collection was 3:4. He gave aways 99 stamps and bought another 18 marbles. The ratio of the stamps to marbles became 3:7. How many stamps were left in Ali's collection.


Appreciate any help. Thanks.

7u = 4u +132 +18
3u = 150
1u = 50
3u = 150 stamps

[3greatkids]

1. Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio 3:2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of the a dictionary.


cost of dictionary - 100%
cost of comics - 120%
220% - $1496
100% - $680
120% - $816

3u - $816
2u - $544 (if bought comics)

$680 - $544 = $136 difference in price between buying the same amt of C or D
$136/$4 = 34 dictionaries
Thus each dictionary is $680/34=$20


2. Marvin bought a box of fruits. 30% of the fruits are apples and the rest oranges. He realised that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found out that there were 52 more fruits in the box. How many fruits were there in the box at first?

30% - apples
70% - oranges

threw half of apple - 30%/2 = 15% of fruits were thrown away

Oranges increase by 40% - 40% x 70% = 28% of fruits were added

28% - 15% = 13% of increase in fruits

13% - 52
100% - 400



3. Ann and Ben were given some money each. If Ann spent $25 each week and Ben spent $75 each week, Ann would still have $1350 left when Ben had sepnt all his money. If Ann spent $75 each week and Ben spent $25 each week, Ann would still have $150 left when Ben had sepnt all his money.

(a) How much money did Ann receive?
(b) How much money did Ben receive?

For every 1 unit Ann spent, Ben spent 2 units more. For every unit Ben spent, Ann spent 2 units more. The total difference in units is 4units between first and second scenario.

$1350 - 150 = $1200
$1200/4= $600
$600/$100= 6 days
6x25 + 1350 = 1500
6x75 = 450