+422 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
+80 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.
+128475 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
