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**

APatel Feb 6, 2019

#1**+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.

itsyaboi Feb 6, 2019

#2**+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

CPhill Feb 6, 2019