Q&A - PSLE Math

[Bunny27]

small:

pixiedust:

Would appreciate some help on this question :


The ratio of the number of $100-notes to $5-notes that David had was 7:4. He exchanged 12 pieces of $100-notes for some $5-notes. After which, the ratio of the number of $100-notes to $5-notes became 1:16. What was the amount of money David had at first ?

Hi,

HTH....

$100-notes : $5-notes ----- 7u : 4u

12 pieces of $100-notes exchanged to $5-notes
12 x 20 = 240 pieces of $5-notes

After which, the ratio of the number of $100-notes to $5-notes became 1:16

$100-notes : $5-notes
7u-12 : 4u+240
1 : 16

cross multiple

16 x (7u-12) = 1 x (4u+240)
112u – 192 = 4u + 240
108u = 432
1u = 4

At first
$100-notes : $5-notes ------- 7u : 4u

Total value of $100-notes ---- 7 x 4 x $100 = $2800
Total value of $5-notes ---- 4 x 4 x $5 = $80

$2800 + $80 = $2880

David had $2880 at first.

Hi, someone pls help on this questions. TIA

1. Mr Yeo spent 1/2 of his money and another $14 more in ShopA.
He went to shop B ans spent 1/3 of his remaining money and another $14 more. In the end, he had $6 left.
How much money did he have at first?

2.Cheryl, Siti and Audrey have some money.
If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money. If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti. Audrey's share is the sum of the other girls.
How much money do they have altogether?

Keep getting $60 for question 1. Not sure is it correct.

Pls advice

[MathIzzzFun]

Hi

Q1.
Work backwards.
$14+$6 = $20 –> 2/3 of remainder
Remainder –> $20/2 x 3 = $30
$30+ $14 = $44 –> 1/2 of money
2 x $44 = $88

cheers.

[Bunny27]

MathIzzzFun:

Hi

Q1.
Work backwards.
$14+$6 = $20 --> 2/3 of remainder
Remainder --> $20/2 x 3 = $30
$30+ $14 = $44 --> 1/2 of money
2 x $44 = $88

cheers.

Hi, need help on this question:


2.Cheryl, Siti and Audrey have some money.
If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money. If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti. Audrey's share is the sum of the other girls.
How much money do they have altogether?

Thanks thanks!

[Gemini11]

Bunny27:

Hi, someone pls help on this questions. TIA

1. Mr Yeo spent 1/2 of his money and another $14 more in ShopA.
He went to shop B ans spent 1/3 of his remaining money and another $14 more. In the end, he had $6 left.
How much money did he have at first?

2.Cheryl, Siti and Audrey have some money.
If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money. If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti. Audrey's share is the sum of the other girls.
How much money do they have altogether?

Keep getting $60 for question 1. Not sure is it correct.

Pls advice

Since MathIzzzFun has already answered your question 1, i'll do question 2 for you.

http://i41.tinypic.com/k2joed.jpg\">

If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money.

Refer to Diagram 1

If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti.

Refer to Diagram 2

So Now we know that 2 units = $3.50 x 4= $ 14

Refer to Diagram 3

So one unit = $14/2
= $7

Therefore we know that cheryl has 3unit- $3.50
= 2 x $ 7 -$3.50 = $17.50

and Siti has 1unit + $3.50 = $7+ $3.50
= $10.50

Given Audrey's share is the sum of the other girls

Therefore Audrey has $17.50 + $10.50 =$28

How much money do they have altogether?

Total = $28 x 2 = $56.

------------------------------------
Hope it Helps

Gemini11 :evil:

[superksmum]

Hi, would someone kindly help in these 2 questions:


a) Julian and Cody have 540 cards althogether. If Cody gives 1/4 of his cards to Julian, and Julian in turn gives 2/5 of his cards to Cody, they will have the same number of cards. how many cards does each boy have at first?

b)There were 756 liters of water in Tank A and Tank B. There were 92 more liters of water in Tank A than in Tank B. The next day, some water was drained off from Tank A and Tank B. The amount of water drained off from Tank A was 1/4 of the amount of water drained off from Tank B. In the end, the amount of water left in Tank B was a third of the amount of water in Tank A. How much water was in Tank A in the end?

Thank you.

[Bunny27]

Gemini11:

Bunny27:

Hi, someone pls help on this questions. TIA

1. Mr Yeo spent 1/2 of his money and another $14 more in ShopA.
He went to shop B ans spent 1/3 of his remaining money and another $14 more. In the end, he had $6 left.
How much money did he have at first?

2.Cheryl, Siti and Audrey have some money.
If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money. If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti. Audrey's share is the sum of the other girls.
How much money do they have altogether?

Keep getting $60 for question 1. Not sure is it correct.

Pls advice

Since MathIzzzFun has already answered your question 1, i'll do question 2 for you.

http://i41.tinypic.com/k2joed.jpg\">

If Cheryl gives $3.50 to Siti, the two girls will have an equal amount of money.

Refer to Diagram 1

If Siti gives $3.50 to Cheryl, Cheryl will have 3 times as much money as Siti.

Refer to Diagram 2

So Now we know that 2 units = $3.50 x 4= $ 14

Refer to Diagram 3

So one unit = $14/2
= $7

Therefore we know that cheryl has 3unit- $3.50
= 2 x $ 7 -$3.50 = $17.50

and Siti has 1unit + $3.50 = $7+ $3.50
= $10.50

Given Audrey's share is the sum of the other girls

Therefore Audrey has $17.50 + $10.50 =$28

How much money do they have altogether?

Total = $28 x 2 = $56.

------------------------------------
Hope it Helps

Gemini11 :evil:

Hi Gemini11，
Appreciated for the models drawing. I can get it now.
Thanks again

[Gemini11]

Bunny27:

Hi Gemini11，
Appreciated for the models drawing. I can get it now.
Thanks again

You r welcome :snuggles:

[small]

superksmum:

Hi, would someone kindly help in these 2 questions:


a) Julian and Cody have 540 cards althogether. If Cody gives 1/4 of his cards to Julian, and Julian in turn gives 2/5 of his cards to Cody, they will have the same number of cards. how many cards does each boy have at first?

Thank you.

Hi,

HTH... (model drawing will be clearer)

At the end, Julian and Cody will have same number of cards

Working backward:
Julian ----- 3u
Cody ----- 2u + 3p

From model drawing:
1u = 3p
3u = 9p

So Julian and Cody ----- 9p x 2 = 18p
Given that total money is $540
18p = 540
1p = 30

if Cody gives 1/4 of his cards to Julian, so before this:
Julian ----- 5u (-1p)
Cody ----- 3p (+1p)


At first:
Julian ----- 5u -1p or (15p – 1p) =14p
Cody ----- 3p + 1p = 4p

Julian-----14 x 30 = 420
Cody ---- 4 x 30 = 120

[small]

superksmum:

Hi, would someone kindly help in these 2 questions:


b)There were 756 liters of water in Tank A and Tank B. There were 92 more liters of water in Tank A than in Tank B. The next day, some water was drained off from Tank A and Tank B. The amount of water drained off from Tank A was 1/4 of the amount of water drained off from Tank B. In the end, the amount of water left in Tank B was a third of the amount of water in Tank A. How much water was in Tank A in the end?

Thank you.

HTH.. (model drawing will be clearer)

At first
Tank A ----- 1unit + 92
Tank B ----- 1unit

2units + 92 = 756
2units = 664
1unit = 332

Thus:
Tank A ----- 424 litres
Tank B ----- 332 litres

Given that the amount of water drained off from Tank A was 1/4 of the amount of water drained off from Tank B.In the end, the amount of water left in Tank B was a third of the amount of water in Tank A

Tank A ----- 424 - 1 part
Tank B ----- 332 - 4 parts

Ratio of Tank B to Tank A is 1 : 3 now

cross multiply
1 x (424 - 1 part) = 3 x (332 - 4 parts)
424 - 1 part = 996 - 12 parts
11 parts = 572
1 part = 52

Tank A ----- 424 - 1 part
Tank A ----- 424 - 52 = 372


Tank A had 372 litres of water in the end

[Gemini11]

superksmum:

Hi, would someone kindly help in these 2 questions:


a) Julian and Cody have 540 cards althogether. If Cody gives 1/4 of his cards to Julian, and Julian in turn gives 2/5 of his cards to Cody, they will have the same number of cards. how many cards does each boy have at first?

Hi i just finished drawing the models for question b when i realised small already answered your question. Anyway, i'll just post up mine
( apparently different method ) should you need it

a) Since given after giving each other some cards the boys will have the same. We shall use these info to work backwards.

540/2= 270

Julian has 270 after giving 2/5 of his to Cody

Therefore, 3 units ---> 270
1 unit --->90
5 units ---> 450

But these 450 cards Julian has, is after he got 1/4 of Cody's card.

Given total cards is 540.

We know Cody has (540-450)= 90 cards, after giving 1/4 his cards to Julian

so, 3 units ---> 90
1 unit ---> 30

how many cards does each boy have at first?

Cody = 90 + 30 = 120 cards
Julian = 450-30 = 420 cards
------------------------------------

Hope it helps

Gemini11 :evil: