Q&A - PSLE Math

[Jwoofamily]

Need help. From 2012 nanyang prelim.


At a swimming meet, school A had 18 more representatives than school B and 6 fewer representatives than school C. The ratio of the number of boys to girls from the three schools was 1:3. The ratios of the number of boys to the number of girls in schools A, B and C were 1:3, 1:5, 2:5 respectively. How many representatives from the three schools were there in all?

Answer in answer key is 96 but I don’t understand how they derive this answer.

Please help show detail workings.
Thanks.

[MathIzzzFun]

MathIzzzFun:

Treelodge:

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:?: Please help! :imdrowning:
Nanyang Prelim 2012 Q18 :slapshead:
Answer given = 96
:thankyou: :thankyou: :thankyou:

alternate approach using concept of multiples and a little Guess & Check..

School B, boys : girls --> 1 : 5 (total 6)
School A, boys : girls --> 1 : 3
School C, boys : girls --> 2 : 5
School A = School B + 18 = School B + 6 x 3
School C = School A + 6 = School B + 6 x 4
Total number of students in School B is a multiple of 6,
So, total number of students in School A is a multiple of 6 and total number of students in School C is also a multiple of 6

School C, boys : girls --> 2 : 5 --> 12 : 30
School A, boys : girls --> 1 : 4 --> 9 : 27 (6 less than C)
School B, boys : girls --> 1 : 5 --> 3 : 15 (18 less than A)
check --> boys: girls = (12+9+3) : (30+27+15) = 24:72= 1:3 √

So,
total number of students = 24 + 72 = 96

cheers.

Need help. From 2012 nanyang prelim.

At a swimming meet, school A had 18 more representatives than school B and 6 fewer representatives than school C. The ratio of the number of boys to girls from the three schools was 1:3. The ratios of the number of boys to the number of girls in schools A, B and C were 1:3, 1:5, 2:5 respectively. How many representatives from the three schools were there in all?

Discussed at pg 797 - see above

cheers

[tianzhu]

Jwoofamily:

Need help. From 2012 nanyang prelim.


At a swimming meet, school A had 18 more representatives than school B and 6 fewer representatives than school C. The ratio of the number of boys to girls from the three schools was 1:3. The ratios of the number of boys to the number of girls in schools A, B and C were 1:3, 1:5, 2:5 respectively. How many representatives from the three schools were there in all?

Answer in answer key is 96 but I don't understand how they derive this answer.

Please help show detail workings.
Thanks.

Hi

Here’s a solution posted earlier in this thread.

I think you can use MD, but I’ll use letters of the alphabet so as to save some time.

Number of representatives in B ------- 1 box
Number of representatives in A ------- 1 box + 18
Number of representatives in C ------- 1 box + 18 + 6

School A
Boys: Girls------- 1A:3A

School B
Boys: Girls ------- 1B:5B

School C
Boys: Girls ------- 2C:5C

1A + 1B + 2C ------ 1p
3A + 5B + 2C ------3p

3A + 3B +6C ------- 3p

3A + 3B +6C ------- 3A + 5B + 2C

Hence, you’ll get 1C ------- 2B

Now change (2C + 5C) to 14B and do a comparison.

14B – 6B (1B+5B) ------- 24

8B ------- 24

B ------- 3

C ------- 6

Number of representatives in C ------- 7*6 ------ 42

Number of representatives in A ------- 42 - 6 ------ 36

Number of representatives in B ------- 18

Total number ------- 96

Best wishes

[ozora]

tianzhu:

ozora:

Need help to identify the number pattern below and find the missing

Number.

4, 6, 8, 12, 24, 36, ___,144, 480

Hi

The missing number is 96.

4*2 ----- 8
6*2 ----- 12
8*3 ------ 24
12*3 ----- 36
24*4 ------ 96
36*4 ------ 144
96*5 ------ 480

Hope this helps

Best wishes

thanks. Really stuck.:)

[Oldschool]

Hi,


BTW, forum admins/mopderators might want to shift this thread under the relevant topics or header.

To begin,

(1) To complete the drawing,

Gogh + Picasso => 4 days, follow by
Picasso => 5 days

(2) Per day, G - P = 1/30 of the drawings

or G = P + 1/30

(3) Therefore, per day,

Gogh + Picasso complete => P + 1/30 + P of the drawings

4 days of (G + P) => 8P + 2/15
5 days of P => 5P

(4) 8P + 2/15 + 5P = 1 complete drawing

then P = 1/15
and G = 1/10

(5) Hence, Gogh will take 10 days whereas Picasso will take 15 days to completes the drawing alone.

Regards

[Oldschool]

Hi,


(1) 2 teams will take 30 days to complete.

Then, 30 days => 100%

So, in 6 days, the 2 teams completed => 100/30 x 6 = 20%

(2) Therefore, left with 80% which was completed by a single team in 40 days.

80% => 40 days
100% => 50 days

(3) Assume that both teams are equally hardworking. Then it would take 50 days for a single team to complete that certain job.

Regards

[MathIzzzFun]

Oldschool:

Hi,


(1) 2 teams will take 30 days to complete.

Then, 30 days => 100%

So, in 6 days, the 2 teams completed => 100/30 x 6 = 20%

(2) Therefore, left with 80% which was completed by a single team in 40 days.

80% => 40 days
100% => 50 days

(3) Assume that both teams are equally hardworking. Then it would take 50 days for a single team to complete that certain job.

Regards

the two team worked at different rate.

Total amount of work to be done --> 30 units (1 day = 1unit of work)

In 6 days, 6 units completed, 24 units left.

Team A (team remained to complete the work) takes 40 days to complete 24 units of work --> 24/40 unit/day = 0.6 unit/day

Team B --> (1 - 0.6) unit/day = 0.4unit /day

Number of days taken by each team to complete all the work by itself:
Team A --> 30/0.6 = 50 days
Team B --> 30/0.4 = 75 days

cheers.

[Oldschool]

MathIzzzFun:

Oldschool:

Hi,


(1) 2 teams will take 30 days to complete.

Then, 30 days => 100%

So, in 6 days, the 2 teams completed => 100/30 x 6 = 20%

(2) Therefore, left with 80% which was completed by a single team in 40 days.

80% => 40 days
100% => 50 days

(3) Assume that both teams are equally hardworking. Then it would take 50 days for a single team to complete that certain job.

Regards

the two team worked at different rate.

Total amount of work to be done --> 30 units (1 day = 1unit of work)

In 6 days, 6 units completed, 24 units left.

Team A (team remained to complete the work) takes 40 days to complete 24 units of work --> 24/40 unit/day = 0.6 unit/day

Team B --> (1 - 0.6) unit/day = 0.4unit /day

Number of days taken by each team to complete all the work by itself:
Team A --> 30/0.6 = 50 days
Team B --> 30/0.4 = 75 days

cheers.

Nice.

[mathnoobs]

MathIzzzFun:

Oldschool:

Hi,


(1) 2 teams will take 30 days to complete.

Then, 30 days => 100%

So, in 6 days, the 2 teams completed => 100/30 x 6 = 20%

(2) Therefore, left with 80% which was completed by a single team in 40 days.

80% => 40 days
100% => 50 days

(3) Assume that both teams are equally hardworking. Then it would take 50 days for a single team to complete that certain job.

Regards

the two team worked at different rate.

Total amount of work to be done --> 30 units (1 day = 1unit of work)

In 6 days, 6 units completed, 24 units left.

Team A (team remained to complete the work) takes 40 days to complete 24 units of work --> 24/40 unit/day = 0.6 unit/day

Team B --> (1 - 0.6) unit/day = 0.4unit /day

Number of days taken by each team to complete all the work by itself:
Team A --> 30/0.6 = 50 days
Team B --> 30/0.4 = 75 days

cheers.

could someone post the question to this answer ? it would be useful.

[superksmum]

Can someone pls help with this question:


Leslie bought some sweets and gave 2/3 of it to Alan. Alan bought some chocolates and gave 2/3 of it to Leslie. Leslie ate 6 chocolates and Alan ate 6 sweets. The ratio of Leslie’s chocolates to sweets became 2:1 and the ratio of Alan’s chocolates to sweets became 4:5. How many sweets did Leslie buy?

Thanks