Rachel and Alice have some sweets. If Rachel gives Alice $10$ pieces of sweet, then they would have the same number of sweets. However, if they both eat $8$ pieces of sweet, Rachel has $3$ times as many pieces of sweet left over as Alice. How many pieces of sweet did they have in total originally? 
Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple