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Friday, August 18 2017 @ 07:45 AM CDT
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 Ratio question- help
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By: Strawberry (offline)  Thursday, September 12 2013 @ 08:25 AM CDT (Read 624 times)  
Strawberry

Swim club and Fit Club had a total of 112 members. Swim Club had 3/5 as many members as Fit Club. During a recruitment exercise, more people joined both clubs. For every 3 members who joined the Swim Club, 1 member joined the Fit Club. Given that the ratio of the number of members in Swim Club to Fit Club in the end was 5:3. find the number of members in each club in the end.

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By: echeewh (offline)  Thursday, September 12 2013 @ 11:50 AM CDT  
echeewh

Hey <Strawberry>,

Following is my worked solution:

<before>
SC : FC
3 : 5

SC: (3/8) × 112 = 42
FC: 112 - 42 = 70

<process - joined>
SC : FC
3 : 1

<after>
5 : 3

42 + 3p = 5u
70 + 1p = 3u

Rearranging these , we have ...

5u - 3p = 42 -- (1)
3u - 1p = 70 -- (2)

Eliminate (p) qty, multiply (2) 3x.

9u - 3p = 210 -- (3)

(3)-(1):
9u - 5u = 210 - 42
4u --> 168
1u --> 42

Number of Members at the end:
SC = 5u --> 5 × 42 = 210
FC = 3u --> 3 × 42 = 126

=========

Trust this helps

Do let me know again if this is different from your <Answerkey> or if there's further clarification.

Cheers,
Edward


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By: Strawberry (offline)  Thursday, September 12 2013 @ 12:50 PM CDT  
Strawberry

Thank you ...

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