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 2009 SA2P6 Anglo Chinese - ratio question --- help
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By: Strawberry (offline)  Thursday, August 16 2012 @ 05:03 AM CDT (Read 854 times)  
Strawberry

8. The ratio of the number of pencils to the number of erasers in a box was 2:3. When 42 pencils were added and 15 erasers were removed, the ratio of the number of pencils to erasers became 3:4. How many erasers were there left in the box?

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By: echeewh (offline)  Thursday, August 16 2012 @ 10:32 PM CDT  
echeewh

Hey Strawberry,

Following pls find my worked solution:

<Cross Multiply method>

<before>
P : E
2 : 3

<process>
P: +42, E: -15

<after>
P : E
3 : 4

(2u + 42) / 3 = (3u - 15) / 4
4 x (2u + 42) = 3 x (3u - 15)
8u + 168 = 9u - 45
9u - 8u --> 168 + 45
1u --> 213

E (left) = 3u - 15 --> (3 x 213) - 15
= 639 - 15 = 624

--- Alternative method (Simultaneous) ----

Use (p) qty for <before> and (u) qty for <after>

2p + 42 = 3u
3p - 15 = 4u

Rearranging above 2 equations, we have...

3u - 2p --> 42 -- (1)
3p - 4u --> 15 -- (2)

Since question is looking for E left at end, we eliminate (p) qty as follows:

(1)x3:
9u - 6p --> 126 -- (3)

(2)x2:
6p - 8u --> 30 -- (4)

(3)+(4):
9u - 8u --> 126 + 30
1u --> 156

E (at end) = 4u --> 4 x 156 = 624

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

Trust the above helps.

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

Cheers,
Edward

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By: Strawberry (offline)  Friday, August 17 2012 @ 12:51 AM CDT  
Strawberry

thanks ... I understand better.

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