Donerick, Luis and Filip shared some sweets. Donerick received 1/11 of the sweets. Luis received 1/4 of the number of sweets Filip received. When Filip gave away 104 sweets to be shared between Donerick and Luis, they found that all of them had the same number of sweets. How many sweets were there at first?
So x = \( {104 * 33 \over 13} = 264\)
So there are 264 seeets at first
Suppose there are x sweets at first,
and Filip has y sweets.
so: (1 - \( {1\over 11}\))x = y + \({1 \over 4}\)y.
\( {1\over 3}\)x = y - 104
=> \( {10 \over 11}x = {5 \over 4} y\) => y = \( {4\over 5} • {10 \over 11}x = {8 \over 11}x\)
Let y = \( {8\over 11}\)x, \( {1 \over 3}x = {8 \over 11}x - 104\)
\({8 \over 11}x - {1 \over 3}x = 104\) => \(({8 \over 11} - {1 \over 3})x = {13 \over 33} = 104\)
