Q&A - PSLE Math

[MathIzzzFun]

MathAche:

Help needed (Nanyang P6 CA1 2011)


Leon bought some terrapins and guppies for a total of $96. He bought 3 times as many guppies as terrapins. He paid $30 more for the terrapins than the guppies. Each terrapin cost $10.40 more than each guppy.
(a) how many terrapins did he buy?
(b) what was the cost of each guppy?

Hi

1 pack of terrapins --> $(96+30)/2 = $63
3 packs of guppies --> $( 63-30) = $33
1 pack of guppies --> $11

$63-$11 = $52 --> 1 pack of terrapins cost $52 more than 1 pack of guppies
$52/$10.40 = 5 --> 5 terrapins/guppies in each pack.

a) number of terrapins --> 5
b) cost of 1 guppy --> $ 11/5 = $ 2.20

cheers.

[MathIzzzFun]

MathAche:

Can anybody recommend a good book about ratios?


Having trouble with this problem because 2 variables change.

INN Store imported Notie mobile phones and Dricsin mobile phones in the ratio 8:5. After selling 120 Notie mobile phones and 135 Dricsin mobile phones, the ratio of Notie mobile phones and Dricsin mobile phones left was 8:3. How many Notie mobile phones did the store import?

Hi

initial + change = final

initial --> Notie: Dricsin = 8u : 5u
final --> Notie : Dricsin = 8p : 3p
8u - 120 = 8p and 5u - 135 = 3p, and then solving for u and p

alternatively, note that ratio for Notie is same before and after and 120 is also divisible by 8

In the end, Notie : Dricsin -> 8 units : 3 units
Initially, Notie -> 8 units + 120 = 8 (1 unit + 15)
So, initially, Dricsin = 5 (1 unit + 15) = 5 units + 75
5 units + 75 - 135 = 3 units
1 unit --> 30
Initially, Notie --> 8 x 30 + 120 = 360

cheers.

[speedmaths.012624com]

MathAche:

Can anybody recommend a good book about ratios?


Having trouble with this problem because 2 variables change.

INN Store imported Notie mobile phones and Dricsin mobile phones in the ratio 8:5. After selling 120 Notie mobile phones and 135 Dricsin mobile phones, the ratio of Notie mobile phones and Dricsin mobile phones left was 8:3. How many Notie mobile phones did the store import?

Hi,

The \"Bags and Boxes Method\" can be used to solve ALL the PSLE Maths problems involving 2 pairs of ratios.
This method can be found in Chapter 2 of the book \"Raffles Maths Tricks - Volume 1\", which has been available at local bookstores since 2006.

Cheers


Speedmaths.com


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[small]

Hi,


Please help and many thanks in advance.

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[tianzhu]

Hi moderator


Good Morning.

To aviod confusion, please help to delete post as my answer is incorrect.

Best wishes.

[mathnoobs]

tianzhu:

Hi small


Good Morning.

Where is this question from?

Jan
Spent ----- 3 units (15 units)
Remaining ------ 7 units (35 units)

Feb
Saved ----- 7 units (1/5*35units)

8*3.95 ------ 31.6

3 parts ----- parents’ tour

5 parts remaining

2 parts ------saved ------- 6219.85
3 parts ------ 6219.85*3/2 ------ 9329.75 ( money given to parents)
8 parts ------ 24879.40

7 units ------ 24879.4+31.6
7 units ------ 24911
50 units ------ 177935.71 (money in the bank at first)

Best wishes

Hi Tianzhu
this is a really hard question to understand. Thanks for the solution.
However, I am confused by these sentences:

Then she purchased 8 pens at $3.95 each. When she heard heard her parents were going on a tour, she gave them 3/8 of he amount she had left.

It looks like she spent the money in March. So the total amount of money spent in March is (8x3.95) + 3 parts. However, from your workings, it looks like she only spent 3 parts in March. :? I can't see how that is done.

[tianzhu]

mathnoobs:

Hi Tianzhu
this is a really hard question to understand. Thanks for the solution.
However, I am confused by these sentences:

Hi

Thank you for reading my solution. You’re certainly a very enthusiastic maths mummy.

For these 7 units in Feb, Nicole spent $31.60 on 8 pens and gave 3 parts of the remainder to her parents. After that, she had 5 parts left. She saved 2 parts (40% of 5 parts).

Hence, we’ll have 2 parts which is equal to $6219.85.

Best wishes

[small]

tianzhu:

Hi small


Good Morning.

Where is this question from?

Jan
Spent ----- 3 units (15 units)
Remaining ------ 7 units (35 units)

Feb
Saved ----- 7 units (1/5*35units)

8*3.95 ------ 31.6

3 parts ----- parents’ tour

5 parts remaining

2 parts ------saved ------- 6219.85
3 parts ------ 6219.85*3/2 ------ 9329.75 ( money given to parents)
8 parts ------ 24879.40

7 units ------ 24879.4+31.6
7 units ------ 24911
50 units ------ 177935.71 (money in the bank at first)

Best wishes

Hi Tianzhu,

As usual, once again many thanks for your solution. This question was extraceted from a Maths Heuristic Assessment of my son.

Will need some time to digest the solution. Btw, I am confused by the '7 units of Jan' and '7 units of Feb'. :oops:

[tianzhu]

small:

Btw, I am confused by the '7 units of Jan' and '7 units of Feb'. :oops:

Hi

Changing percentages into units and using equivalent ratios for the month of Jan.

30% ------ 3 units ------- 15 units
70% ------ 7 units ------- 35 units.

In Feb, the amount saved is 1/5*35 units ------ 7 units.

Best wishes

[small]

Hi Tianzhu,


Finally I understood the solution.

I misinterpreted the question as I thought Nicole saved 7 units in Feb, then the balance which is 28 units, she spent $31.60 for 8 pens and gave 3/8 of (28units – 31.60) to her parents in March; 40% of the remainder is $6219.85.


In fact it should be:
Nicole spent 30% and saved 70% in Jan; After spending in Feb, she saved 14% (1/5 of 70%). For this 14%, Nicole spent $31.60 on 8 pens and gave 3 units of the remainder to her parents, she left with 5 units now and saved 2 units (40% of 5 units), and this 2 units equal to $6219.85

a)\t
2U ----- 6219.85
3U ----- 9329.775

b)
2U ----- 6219.85
8U ----- 24879.40

14% ----- 24879.40 + 31.60
14% ----- 24911
100% ----- 177 935.71