The total money never changes, so split it into 20 equal units. Sam is $$\frac{1}{4}$$ = 4 units before (1 : 4) and $$\frac{9}{11}$$ = 9 units after (9 : 11). The $60 he received is the extra 5 units.<br><br>[[model:questions/solutions/q5292.png]]<br><br>• Sam’s gain → 9 units − 4 units = 5 units = $60<br>• 1 unit → $60 ÷ 5 = $12<br>• Sam in the end → 9 units = 9 × $12 = $108<br><br>Sam has $108 in the end.<br>Check: total 20 units = $240; after Sam $108, Patrick $132 = 9 : 11. ✓