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The ratio of Og's clubs to skins is 5:3, if he trades 4 of his clubs for 2 more skins, the ratio of clubs to skins will be 8:7. How many more clubs than skins does Og have before any trading occurs?
 

Answer Choices

A.  8

B.  9

C.  10

D.  12

 Feb 6, 2019
 #1
avatar+79 
+2

x/y = 5/3

and

x-4/y+2 = 8/7

 

So, x = 5/3y

 

\(\frac{\frac{5y}{3}-4}{y+2}=\frac{8}{7}\)

 

Solving this, we should get that y=12 and x=20

 

So, Og has 8 more.

 Feb 6, 2019
 #3
avatar+100578 
0

Nice job, itsyaboi !!!

 

 

cool cool cool

CPhill  Feb 6, 2019
 #2
avatar+100578 
+1

C / S   =  5/3    ⇒    C = (5/3)S       (1)

 

[ C - 4] / [ S + 2]  =  8/7               (2)

 

 

Sub (1) into (2)

 

[ (5/3)S - 4 ] / [ S + 2 ]   =  8/7            cross-multiply

 

7 [ (5/3)S - 4 ] =   8[ S + 2 ]        simplify

 

(35/3)S - 28  = 8S + 16

 

(35/3)S - 8S =  16 + 28

 

(35/3)S - (24/3)S = 44

 

(11/3)S = 44

 

S =  (3/11) *44 =    12

 

So....the number of original clubs =  (5/3)S =   20

 

So....he has 20 - 12 =  8 more

 

 

cool cool cool

 Feb 6, 2019

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