Q&A - PSLE Math

[Apphia]

1) Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in the Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If the water from Tank X is poured into Tank Y until the water reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?


2) Julian had 300 more cards than Faizal. Julian gave 3/5 of his cards to Faizal. Faizal then gave 1/4 of the total number of what he had then to Julian. In the end, Fazial had 300 more cards than Julian. How many cards did Julian have at first? :?:

Many thanks in advance.

Apphia

[tianzhu]

anneshirleygilbert:

Hello tianzhu,
Like ozora, \"I'm stuck.\" I can see how area of A would be 20 units, but how did you get the breakdown for B to be 15 units and C to be 1 unit? Been trying to crack it all weekend. It's like a bone in my throat. Please help.

Hi anneshirleygilbert

Good Afternoon.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5015/5525151537_f2a37c10f9_b.jpg\">

[Dharma]

anneshirleygilbert:

Thank you, Dharma. You're so kind to offer two options in the solutions. Understand both of them. Was just wondering, is this level of math expected of Spore P5/P6 students preparing for PSLE? Seems quite a tall order to me.


Appreciate your help.

Hi anneshirleygilbert,

The 1st method uses fractions and the 2nd method uses ratio. (both are P5/6 topics )

The most important thing is to utilize the relationship between areas of A and areas of (B + C) which is given in the question.

[ozora]

Dharma:

anneshirleygilbert:

[quote=\"tianzhu\"]
Hi

You’ve started correctly, but how about this condition?

The total area of B and C is 4/5 that of A.

Best wishes

Hello tianzhu,
Like ozora, \"I'm stuck.\" I can see how area of A would be 20 units, but how did you get the breakdown for B to be 15 units and C to be 1 unit? Been trying to crack it all weekend. It's like a bone in my throat. Please help.

Area B + C = 4/5 of Area of A
Area of A = 5/4 of Area of (B + C) = 5/4 of B + 5/4 of C ----------- ( 1 )

Shaded area of A = Shaded areas of (B + C)
1/6 of A = 1/5 of B + 1/3 of C
6/6 of A = 6/5 of B + 6/3 of C ------------- ( 2 )

Equating ( 1 ) and ( 2 )
5/4 of B + 5/4 of C = 6/5 of B + 6/3 of C
5/4 of B – 6/5 of B = 6/3 of C – 5/4 of C
25/20 of B – 24/20 of B = 24/12 of C – 15/12 of C
1/20 of B = 9/12 of C
B = 15C

A = 5/4 (15C + C) = 20C

Ratio of areas of A : B : C = 20 : 15 : 1


OR


B ( shaded ) : B ( unshaded ) = 1 : 4 => 1u : 4u
C ( shaded ) : C ( unshaded ) = 1 : 2 => 1p : 2p
A (shaded ) : A ( unshaded ) = 1 : 5 = (1u + 1p) : (5u + 5p)

Total area of (B + C ) = 5u + 3p
Total area of A = 6u + 6p

Total area of (B + C) = 4/5 of total area of A
5u + 3p = 4/5(6u + 6p)
25/5u – 24/5u = 24/5p – 15/5p
1u = 9p

Ratio of A : B : C = (6u + 6p) : 5u : 3p = 60p : 45p : 3p = 20 : 15 : 1[/quote]Thanks Dharma
I only manage to equate eq 1 but not 2.
more to learn

[ozora]

tianzhu:

anneshirleygilbert:

Hello tianzhu,
Like ozora, \"I'm stuck.\" I can see how area of A would be 20 units, but how did you get the breakdown for B to be 15 units and C to be 1 unit? Been trying to crack it all weekend. It's like a bone in my throat. Please help.

Hi anneshirleygilbert

Good Afternoon.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5015/5525151537_f2a37c10f9_b.jpg\">

tianzhu thanks for the model. is really great help

[Hifive]

Hi


Need help on this question:

Ahmad has 50% more money than Bernard, Bernard has 20% more money than Clement. After Ahmad gives Bernard and Clement a total of $350, and Bernard gives Clement $400, the ratio of Ahmad’s money to Bernard’s money to Clement’s money becomes 1:1:3. How much money did Ahmad give to Bernard?

Thanks in advance.

[MathIzzzFun]

anneshirleygilbert:

tianzhu:

[quote=\"ozora\"]
then i am stuck.
using your method.
I had the following:
Circle A: shaded= 1u ; unshaded=5 u; total : 6units
Circle B: shaded= 1u ; unshaded=4 u; total : 5units
Circle C:: shaded= 1u ; unshaded=2 u; total : 3units

area of A: Area of B: Area of C
6:5:3
unless i missed out the steps?

Hi

You’ve started correctly, but how about this condition?

The total area of B and C is 4/5 that of A.

Best wishes

Hello tianzhu,
Like ozora, \"I'm stuck.\" I can see how area of A would be 20 units, but how did you get the breakdown for B to be 15 units and C to be 1 unit? Been trying to crack it all weekend. It's like a bone in my throat. Please help.[/quote]Hi

Here is another way to solve using models. Hope it helps.


http://postimage.org/image/2qt28km10/


cheers.

[tianzhu]

Hi Hifive


Good Morning.

This question touches on internal transfer among Ahmad, Bernard and Clement.

Therefore the total amount of money remains the same before and after. Remember to choose the right base for the comparison. Once done and using the Units Method, you are on the way to the answer.

Hope this helps.

Best wishes

http://farm6.static.flickr.com/5251/5528295470_523bb77e56_b.jpg\">

[tianzhu]

Hi


Good Morning

This question touches on two scenarios involving ‘double if”.

Once a student is able to see that the difference in volumes in two tanks is equal to 18 litres which is the difference between 26 and 8, the rest of the answer comes into place.

Hope this helps.

Best wishes.

http://farm6.static.flickr.com/5136/5528571093_6f56b0c534_b.jpg\">

[Hifive]

Hi tianzhu


Thanks so much for your explanation and answer.

Have a nice day!