The teacher gave three students the same amount of money to buy stationery. A bought 3 pens and has $3 left. B bought 5 crayons and has $5 left. C bought 7 pencils and has $3 left. If the price for each item is an integer, what is the least total amount of money the teacher gave them?

Let the price of each type of pens purchased by A,B,C be a,b,c respectively $

=>3a+3=5b+5=7c+3

=> the amount the teacher gives to each student is divisible by 3 and 5

=> the amount is in the form of 15k

there are 15≡1(mod 7)

=>15k≡k(mod 7) where 15k divided by 7 leaves a remainder of 3

=>k smallest is k=3

=> total amount is 15.3.3=135