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[Vanilla Cake]

clblinym:

Mrs Wong is preparing gifts for the coming party.

She buys 540 notepads, 720 pens and 900 pencils.
The total cost of each type of stationery is equal.
She divides the notepads equally into red boxes, pens equally in yellow gift boxes and pencils equally in blue gift boxes.
She wishes that the cost of each gift box is equal and as low as possible.
Find the number of notepads she needs to put in each red gift box.

My working:

A  Notepad
B  Pen
C  Pencil

Ratio of number
A: B : C
3 : 4: 5

The LCM of 3,4 and 5 is 60.

3 x 4 = 12
4 x 5 = 20
3 x 5 = 15

Ratio of cost per item
A: B: C
20:15:12  Cost
3 : 4: 5  Number put in each box

For the cost of each gift box to be equal, the cost multiplied by the number should result in same answer for all 3 cases.

20x3=60
15x4=60
12x5=60

Answer: 3

Dharma:

Let unit cost of notepads, pens and pencils be a, b and c
540a = 720b = 900c (Total cost of each type of stationery is the same)

Since the cost of each gift box is equal;
3a = 4b = 5c (Lowest cost for each gift box; number of gifts in each box must be lowest possible) since the unit cost for each type of gift does not change.

Number of note pads = 3

Alternative http://www.onsponge.com/forum/35-thinkingmathonsponge/6568-p6-math-olympiad.html from OnSponge forum for this question from SMOPS 2005 1st round - Q30.

[clblinym]

Vanilla Cake:

clblinym:

Mrs Wong is preparing gifts for the coming party.

She buys 540 notepads, 720 pens and 900 pencils.
The total cost of each type of stationery is equal.
She divides the notepads equally into red boxes, pens equally in yellow gift boxes and pencils equally in blue gift boxes.
She wishes that the cost of each gift box is equal and as low as possible.
Find the number of notepads she needs to put in each red gift box.

My working:

A  Notepad
B  Pen
C  Pencil

Ratio of number
A: B : C
3 : 4: 5

The LCM of 3,4 and 5 is 60.

3 x 4 = 12
4 x 5 = 20
3 x 5 = 15

Ratio of cost per item
A: B: C
20:15:12  Cost
3 : 4: 5  Number put in each box

For the cost of each gift box to be equal, the cost multiplied by the number should result in same answer for all 3 cases.

20x3=60
15x4=60
12x5=60

Answer: 3

Dharma:

Let unit cost of notepads, pens and pencils be a, b and c
540a = 720b = 900c (Total cost of each type of stationery is the same)

Since the cost of each gift box is equal;
3a = 4b = 5c (Lowest cost for each gift box; number of gifts in each box must be lowest possible) since the unit cost for each type of gift does not change.

Number of note pads = 3

Alternative http://www.onsponge.com/forum/35-thinkingmathonsponge/6568-p6-math-olympiad.html from OnSponge forum for this question from SMOPS 2005 1st round - Q30.

Hi, Vanilla Cake

Thank you very much.

Regards,
Amy

[clblinym]

Hi, Can anyone help to solve the problems below. Thank you.


1) There are buses travelling to and fro between Station A and Station B. The buses leave the stations at regular interval and a bus will meet another bus coming in the opposite direction every 6 minutes.
Peter starts cycling from A towards B at the same time Jane starts cycling from B towards A.
Peter and Jane will meet a bus coming in the opposite direction every 7 and 8 minutes respectively.
After 56 minutes of cycling on the road, they meet each other.
Find the time taken by a bus to travel from A to B.
Answer : 68

2)


http://postimage.org/image/1ww3enfvo/
Answer : 666


Thank you for your time and effort.
Amy

[cchew]

clblinym:

1) There are buses travelling to and fro between Station A and Station B. The buses leave the stations at regular interval and a bus will meet another bus coming in the opposite direction every 6 minutes.
Peter starts cycling from A towards B at the same time Jane starts cycling from B towards A.
Peter and Jane will meet a bus coming in the opposite direction every 7 and 8 minutes respectively.
After 56 minutes of cycling on the road, they meet each other.
Find the time taken by a bus to travel from A to B.
Answer : 68

Solution was posted by mathsguru on 24/11/2009 21:03 refer to the link below:
http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6373&postdays=0&postorder=asc&start=90

[SoWoW]

i have 2 P5 maths questions to ask the experts here… Please help


1) A coin box contained some twenty cent and fifty -cent coins in the ratio 4:3. After 20 twenty-cent coins were taken out to exchange for fifty-cent coins of the same value and put back in the box, the ratio of the number of twenty-cent coins to the number of fifty-cent coins became 7:11. find the sum of money in the box.

2) There were 280 people at a concert. 1/4 of the males and 1/5 of the females wore glasses. Given that a total of 60 people wore glasses in the concert, how many females wore glasses?

[clblinym]

cchew:

clblinym:

1) There are buses travelling to and fro between Station A and Station B. The buses leave the stations at regular interval and a bus will meet another bus coming in the opposite direction every 6 minutes.
Peter starts cycling from A towards B at the same time Jane starts cycling from B towards A.
Peter and Jane will meet a bus coming in the opposite direction every 7 and 8 minutes respectively.
After 56 minutes of cycling on the road, they meet each other.
Find the time taken by a bus to travel from A to B.
Answer : 68

Solution was posted by mathsguru on 24/11/2009 21:03 refer to the link below:
http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=6373&postdays=0&postorder=asc&start=90

Hi, cchew
Thank you very much for the sharing.
Amy

[clblinym]

SoWoW:

i have 2 P5 maths questions to ask the experts here.. Please help


1) A coin box contained some twenty cent and fifty -cent coins in the ratio 4:3. After 20 twenty-cent coins were taken out to exchange for fifty-cent coins of the same value and put back in the box, the ratio of the number of twenty-cent coins to the number of fifty-cent coins became 7:11. find the sum of money in the box.

2) There were 280 people at a concert. 1/4 of the males and 1/5 of the females wore glasses. Given that a total of 60 people wore glasses in the concert, how many females wore glasses?

Dear Sowow,

This is my answer and working for question 1.

20 x 20 cents = $4.00
$4.00/50 cents = 8

20 20-cent coins were taken out.
8 50-cent coins were put in.

At first, ratio was 4:3.
After that, the ratio was 7:11.

4:3 = 8:6

If it was 8:6 at first,
1u is 20,
5u is 8 (wrong)

4:3= 12:9

5u is 20,
2u is 8
(correct)
1u is 4.

The ratio at first was 12:9.

12u is 48.
48 x 20cents = $9.60

9u is 36.
36 x 50cents = $18

$18 + $9.60 is $27.60

Ans: $27.60

Can you check whether $27.60 is the answer please?

Thanks.

Amy

[YLH88]

SoWoW:

i have 2 P5 maths questions to ask the experts here.. Please help


2) There were 280 people at a concert. 1/4 of the males and 1/5 of the females wore glasses. Given that a total of 60 people wore glasses in the concert, how many females wore glasses?

Hi SoWoW,

I'm not expert but just trying to help. Please check the answer key if the answer for qn 2 is 40.

For Qn 2,

Total = 280

Total Male = 4u --> male with glasses = 1u, male without glasses = 3u

Total Female = 5p --> female with glasses = 1p, female without glasses = 4p

4u + 5p = 280 --> total no of people
4u = 280 - 5p

1u + 1p = 60 --> total people with glasses
4u + 4p = 240
4u = 240 - 4p

280 - 5p = 240 - 4p
280 - 240 = 5p - 4p
40 = p --> females with glasses

[clblinym]

SoWoW:

i have 2 P5 maths questions to ask the experts here.. Please help


1) A coin box contained some twenty cent and fifty -cent coins in the ratio 4:3. After 20 twenty-cent coins were taken out to exchange for fifty-cent coins of the same value and put back in the box, the ratio of the number of twenty-cent coins to the number of fifty-cent coins became 7:11. find the sum of money in the box.

2) There were 280 people at a concert. 1/4 of the males and 1/5 of the females wore glasses. Given that a total of 60 people wore glasses in the concert, how many females wore glasses?

Dear SoWow,

This is my answer for the 2nd question.

1/4 of males and 1/5 of females --> 60
4/4 of males and 4/5 of females --> 240
1/5 of females --> 280-240
= 40

1/5 of females (40) wore glasses.


Thanks.

Amy

[Vanilla Cake]

clblinym:

http://postimage.org/image/1ww3enfvo/

Answer : 666

Hi Amy,
Below is the solution worked out by my P5 younger sister:
Look at the number carefully and you will see the number pattern:
Bottom row (fifth row): 1,2,6,24,120
Fourth row: 2,6,24,120
Third row: 6,24,120
2nd row: 24,120
Top row (1st row): 120

Bottom row:
1x2=2
2x3=6
6x4=24
24x5=120

Numbers from the fourth row are taken form the 2nd to last numbers of the bottom row.

Numbers from the third row are taken from the 2nd to last numbers of the fourth row.

Use the same pattern and apply to 2nd and top row.

So, value of X = 6+6+6+24+24+120+120+120+120+120=666

Are you a parent or a P5 student?