James bought some cans of sardines and tuna in the ratio of 4:5. A total of 22 cans of sardines and 1/2 of the cans of tuna were used. In the end, the ratio of the cans of sardines to the cans of tuna became 1:2. Find the number of cans of sardines that James bought at first.
Suppose james bought x cans of sardines & y cans of tuna
x/y = 4/5
∴ x = 4/5y -- (1)
A total of 22 cans of sardines & y/2 cans of tuna were used
∴ (x - 22)/y/2 = 1/2
∴ x - 22 = y/4 -- (2)
from (1) & (2)
4/5y - 22 = y/4
∴ 4y/5 - y/4 = 22
∴ 16y - 5y = 22 * 20
∴ y = 40
∴ x = 4/5 * 40
∴ x = 32 cans
