Q&A - PSLE Math

[tianzhu]

brastilava:

Hi Tianzhu,


Thank-you for your prompt reply. I was trying to figure out why after burning 4 units in candle A and 5 units in Candle B, the ratio of remaining candle A: candle B is 2:1. What I meant is that how do I know to draw 6 boxes in the first place for both candles?

Hi

You may look at it this way.

The candles A and B are of equal length.

A common multiple of 4 and 5 is 20.

Assuming the candle is 20 units long.

20/5 ------ 4 units (A)
20/4 ------ 5 units (B)

We are asked to find how long it takes for Candle A to be twice as long left as Candle B.

Hence, candle A ------ 2p and candle B ------ 1p

We'll use parts(p) to differentiate the \"burnt\" portion of the candles from the \"unburnt\" portion.

First we draw 4 units to show the “burnt” portion of candle A and 5 units to show the “burnt” portion of candle B.

As the candles are of equal length, we have in this particular case, 1p = 1 unit.This gives a total of 6 units or 6 parts as the length of each candle.

Best wishes

[Nebbermind]

Just curious....they r to solve this 5 marks qn in how many mins? :scratchhead:

[brastilava]

Hi Tianzhu,


Thank-you so much for your explanation:)

[tianzhu]

brastilava:

Hi Tianzhu,


Thank-you so much for your explanation:)

Hi

You're welcome.

Here's another question on \"candle burning rate\" if you want your child to have more practice.

Two candles of the same height are lit at the same time. The first candle takes 5h to burn completely. The second candle takes 4h to burn completely. If each candle burns at a constant rate, how long does it take, in hours, for the height of the first candle to be four times that of the second candle?(ans --- 3 3/4)

Best wishes

[Nebbermind]

The candles solution looks so abstract…prob coz I donch have any heuristic background.


Building on what TZ has provided, I looked at it from another angle.

Let length of both candles by 20U.

Rate of burning for A & B are 4U/hr and 5U/hr respectively.

If T is the time taken, then

Length of A left = 20U - 4UT
Length of B left = 20U - 5UT

Since A is twice as long,

2*[20U - 5UT] = 20U - 4UT
=> 40U -10UT = 20U - 4UT
=> 20U = 6U*T
=> T = 20/6 = 3 1/3

[MathIzzzFun]

Nebbermind:

The candles solution looks so abstract...prob coz I donch have any heuristic background.


Building on what TZ has provided, I looked at it from another angle.

Let length of both candles by 20U.

Rate of burning for A & B are 4U/hr and 5U/hr respectively.

If T is the time taken, then

Length of A left = 20 - 4U*T
Length of B left = 20 - 5U*T

Since A is twice as long,

2*[20 - 5U*T] = 20U - 4U*T
=> 40U -10U*T = 20U - 4U*T
=> 20U = 6U*T
=> T = 20/6 = 3 1/3

hi

If we see the question as similar to this - http://www.flickr.com/photos/62167097@N02/5703951396/in/photostream, then it would not be as confusing.

or another question:
\"Mary and Charles had the same amount of money. After Mary spent 4/5 as much as Charles, Mary had twice as much as Charles had left. What fraction of Mary's money did she spend?\"

cheers.

[kiasuaunt]

MathIzzzFun:

Nebbermind:

The candles solution looks so abstract...prob coz I donch have any heuristic background.


Building on what TZ has provided, I looked at it from another angle.

Let length of both candles by 20U.

Rate of burning for A & B are 4U/hr and 5U/hr respectively.

If T is the time taken, then

Length of A left = 20 - 4U*T
Length of B left = 20 - 5U*T

Since A is twice as long,

2*[20 - 5U*T] = 20U - 4U*T
=> 40U -10U*T = 20U - 4U*T
=> 20U = 6U*T
=> T = 20/6 = 3 1/3

hi

If we see the question as similar to this - http://www.flickr.com/photos/62167097@N02/5703951396/in/photostream, then it would not be as confusing.

or another question:
\"Mary and Charles had the same amount of money. After Mary spent 4/5 as much as Charles, Mary had twice as much as Charles had left. What fraction of Mary's money did she spend?\"

cheers.

What's the ans? Thanks.

[tianzhu]

kiasuaunt:

What's the ans? Thanks.

Hi

Mary and Charles had the same amount of money. After Mary spent 4/5 as much as Charles, Mary had twice as much as Charles had left. What fraction of Mary's money did she spend?\"

If you are talking about this question, the answer is 2/3.

Mary
Spent ------ 4 units
Left ------ 2 parts

Charles
Spent ------ 5 units
Left ------ 1 part

4 units + 2 parts ------ 5 units + 1 part

Hence, 1 unit ------ 1 part

4/6 ------ 2/3

Best wishes

[pixiedust]

Hi all,


I can work out the Mary and Charles as the clue given is 'spent 4/5 as much'.
However, for the first burning candles question, I have difficulties with the burning rate ( u and p, I am ok).

Candle A -> 1hr 1/5 of candle burnt
Candle B -> 1hr 1/4 of candle burnt
why burning rate is A:B 4:5 ?

something similar to inversely proportional for speed questions ?

[tianzhu]

pixiedust:

Hi all,


I can work out the Mary and Charles as the clue given is 'spent 4/5 as much'.
However, for the first burning candles question, I have difficulties with the burning rate ( u and p, I am ok).

Candle A -> 1hr 1/5 of candle burnt
Candle B -> 1hr 1/4 of candle burnt
why burning rate is A:B 4:5 ?

something similar to inversely proportional for speed questions ?

Hi

The candles A and B are of equal length.

A common multiple of 4 and 5 is 20.

Assuming the candle is 20 units long.

20/5 ------ 4 units (A)

20/4 ------ 5 units (B)

Hence A:B ------ 4:5

Best wishes