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 Henry Park Maths Paper 2011 sa2 paper2 Q18
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By: sunshine0809 (offline)  Monday, July 09 2012 @ 09:27 PM CDT (Read 1277 times)  
sunshine0809

Hi ,
Can anyone help me to solve Henry park Maths 2011 sa2 ,paper 2, Q18?
18. A large warehouse had a total of 2180 black,red and white t-shirts for sale.The ratio of the number of black T-shirts to the number of red T-shirts was 3:1 . After 2/5 of the black T-shirts, 1/3 of the white T-shirts and none of the red T-shirts were sold on the first day,there were 1504 T-shirts left. How many red T-shirts did the warehouse have at first?
Thank You

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By: echeewh (offline)  Tuesday, July 10 2012 @ 07:06 PM CDT  
echeewh

Hey sunshine,

Pls find my worked solution as follows:

<Before>
B : R
3 : 1

W - 1 whole

<Process>
Sold (2/5) B, none R, (1/3) W

<After>
B : R
9/5 : 1 -- (x5)

W - (2/3)

(splitting 1p into 5u each)
B : R
9 : 5

Hence do likewise for <Before> ratio.

<Before>
B : R
15: 5

W - 1 whole


Given that there were 2180 (B,R,W) T-shirts at first, and 1504 (B,R,W) left, we have ...

20u + 1W --> 2180 --- (1)
14u + (2/3)W --> 1504 --- (2)

Eliminating W:
(2)x(3/2):

21u + 1W --> 2256 --- (3)

Comparing (1),(3):
(3)-(1):

21u - 20u --> 2256 - 2180
1u --> 76

Number of R T-shirts at first = 5u --> 5 x 76
= 380

================================

Trust this helps.

Do let me know again if there's any clarification.

Cheers,
Edward

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