The ratio of Nathan's cherries to Shane's cherries was 9:2. After Nathan ate 32 cherries, the ratio became 1:2. How many cherries did Nathan have at first?
+128406 Call the total nuber of cherries . N
Nathan started with (9) /(9 + 2) = 9/11 of them
And Shane had (2/11) of them
So
(9/11) N - 32 1
____________ = ___ cross-multiply
(2/11)N 2
2 [ (9/11)N - 32 ] = (2/11)N
(18/11 ) N - 64 = (2/11)N
(18/11)N - ( 2/11)N = 64
(16/11)N = 64
N = 64 ( 11 / 16) = 44 = total number
Natan started with (9/11) (44) = 36
