Let's understand this problem step by step. Mom has 3 fifty-yuan bills and 2 twenty-yuan bills, which gives her a total of 190 yuan. She needs to buy a backpack for 128 yuan and a pencil case for 27 yuan.
Now let's see what happens with the first payment. Mom pays with 1 fifty-yuan bill and 2 twenty-yuan bills. That's 50 plus 20 plus 20, which equals 90 yuan. But the total cost is 128 plus 27, which is 155 yuan. So she still needs to pay 155 minus 90, which is 65 yuan more.
现在我们需要算出妈妈还需要几张50元纸币来付剩下的65元。我们想想：如果用1张50元，那就是50元，比65元少，不够用。如果用2张50元，那就是100元，比65元多，够用了。所以妈妈至少需要再付2张50元纸币。找零就是100减65等于35元。
最后我们来算算妈妈还剩多少钱。妈妈原来有190元，她买书包花了128元，买文具盒花了27元，总共花费155元。所以妈妈最后还剩190减155等于35元。这35元就是她买完东西后剩下的钱。