Q&A - PSLE Math

[iFruit]

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Bill increased by 33 1/3 % means it increased by a third. So the total price after the mistake = 1 1/3 of total price before mistake = 4/3 of total price before mistake

Let cost of leather shoe = C
Then cost of canvas shoe = = C/2.5 = 2C/5

Number of pairs of leather shoes = 5
Let Number of pairs of canvas shoes = n

total cost before the mistake = 5C + n*2C/5 = C (5 + 2n/5)

total cost after the mistake = nC + 5*2C/5 = nC + 2C = C (n+2)

4/3 * C(5 + 2n/5) = C(n+2)

4/3 * (5 + 2n/5) = (n+2)

20 + 8n/5 = 3n + 6

14 = 3n - 8n/5 = 7n/5---> n =10

ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes = 10:5 = 2:1

HTH

[JadeDry]

iFruit:

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Bill increased by 33 1/3 % means it increased by a third. So the total price after the mistake = 1 1/3 of total price before mistake = 4/3 of total price before mistake

Let cost of leather shoe = C
Then cost of canvas shoe = = C/2.5 = 2C/5

Number of pairs of leather shoes = 5
Let Number of pairs of canvas shoes = n

total cost before the mistake = 5C + n*2C/5 = C (5 + 2n/5)

total cost after the mistake = nC + 5*2C/5 = nC + 2C = C (n+2)

4/3 * C(5 + 2n/5) = C(n+2)

4/3 * (5 + 2n/5) = (n+2)

20 + 8n/5 = 3n + 6

14 = 3n - 8n/5 = 7n/5---> n =10

ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes = 10:5 = 2:1

HTH

Thanks, that helps a lot.

[tianzhu]

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

Hi

This is an interesting question, haven't seen such question from past years papers.

Best wishes

[kim2410]

Haha, my cousin took PSLE this year, she say too easy. Oh gosh, means next year is prob going to be REALLY hard! Good luck to all 2011 candinates, better start studying NOW!

[Dharma]

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

L(5u) + C(2u) = 300 ---------- (1)
L(2u) + C(5u) = 400 ---------- (2)

7L(1u) + 7C(1u) = 700 --------(1) + (2) = (3)
L(1u) + C(1u) = 100 ------- (3) divide by 7 = (4)

L(2u) + C(2u) = 200 -----------(5) = (4) x 2

L(3u) = 100 -------------- (1) – (5)
3u = 100/5
1u = 100/15

1u(L +C ) = 100
L + C = 100/(100/15) = 15
C = 15 – 5 = 10
Ratio => 10 : 5 = 2 : 1

[Brenda10]

kim2410:

Haha, my cousin took PSLE this year, she say too easy. Oh gosh, means next year is prob going to be REALLY hard! Good luck to all 2011 candinates, better start studying NOW!

I heard this comment too. However, usually Maths tough then Science will be easy.

[JadeDry]

Dharma:

JadeDry:

Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

L(5u) + C(2u) = 300 ---------- (1)
L(2u) + C(5u) = 400 ---------- (2)

7L(1u) + 7C(1u) = 700 --------(1) + (2) = (3)
L(1u) + C(1u) = 100 ------- (3) divide by 7 = (4)

L(2u) + C(2u) = 200 -----------(5) = (4) x 2

L(3u) = 100 -------------- (1) – (5)
3u = 100/5
1u = 100/15

1u(L +C ) = 100
L + C = 100/(100/15) = 15
C = 15 – 5 = 10
Ratio => 10 : 5 = 2 : 1

Thank you Dharma, this helps a lot.

But one small question if I may-What does \"u\" stand for?

[Dharma]

JadeDry:

Dharma:

[quote=\"JadeDry\"]Hello Again.


I have another question which I would like some help on.

Mr Sim instructed his assistant to place an order for 5 pairs of leather shoes and a number of pairs of canvas shoes. A pair of leather shoes costs two and a half times as much as a pair of canvas shoes. His assistant made a mistake in the order and the number of pairs of the two types of shoes had been interchanged. This increased the bill by 33 1/3%

Find the ratio of the number of pairs of canvas shoes to the number of pairs of leather shoes in the order that Mr Sim instructed his assistant to place.

I have tried solving it but cannot go further than a few steps, any help would be greatly appreciated.

Thanks in advance.

L(5u) + C(2u) = 300 ---------- (1)
L(2u) + C(5u) = 400 ---------- (2)

7L(1u) + 7C(1u) = 700 --------(1) + (2) = (3)
L(1u) + C(1u) = 100 ------- (3) divide by 7 = (4)

L(2u) + C(2u) = 200 -----------(5) = (4) x 2

L(3u) = 100 -------------- (1) – (5)
3u = 100/5
1u = 100/15

1u(L +C ) = 100
L + C = 100/(100/15) = 15
C = 15 – 5 = 10
Ratio => 10 : 5 = 2 : 1

Thank you Dharma, this helps a lot.

But one small question if I may-What does \"u\" stand for?[/quote]Units - represents the cost of shoes
1 pair of Leather shoes costs 5u
1 pair of Canvas shoes costs 2u

[noob]

Hi Dharma and tianzhu, need your help to solve following question:-


Alice, Betty and Cecilia shared the cost of a present. Alice paid 1/3 of the total amount of money paid by Betty and Cecilia. Betty paid 1/8 of the amount of money paid by Alice and Cecilia. Alice paid $60 less than Cecilia.
(a) How much did Betty pay?
(b) What was the cost of the present?

[JadeDry]

Dharma:

JadeDry:

[quote=\"Dharma\"]
L(5u) + C(2u) = 300 ---------- (1)
L(2u) + C(5u) = 400 ---------- (2)

7L(1u) + 7C(1u) = 700 --------(1) + (2) = (3)
L(1u) + C(1u) = 100 ------- (3) divide by 7 = (4)

L(2u) + C(2u) = 200 -----------(5) = (4) x 2

L(3u) = 100 -------------- (1) – (5)
3u = 100/5
1u = 100/15

1u(L +C ) = 100
L + C = 100/(100/15) = 15
C = 15 – 5 = 10
Ratio => 10 : 5 = 2 : 1

Thank you Dharma, this helps a lot.

But one small question if I may-What does \"u\" stand for?

Oh I see...Thank you.

Units - represents the cost of shoes
1 pair of Leather shoes costs 5u
1 pair of Canvas shoes costs 2u[/quote]