3. a sum of $2700 is to be given in the form of 63 prizes. if the prize is of either $100 or $25, find the number of prizes of each type.

There has to be a total of 63 boxes each with a prize in them.

There are two types of prizes: The first type is $25 and second type is $100. 

If you make all the prizes $100, you will only end up with 27 prizes. ($2700 / 100), which is too little. 

If you make all the prizes $25, you will only end up with 108 prizes ($2700/ 25), which is too way many. 

The answer has to be combination of prizes More $25 prizes will have an outcome of more prizes in total. 
More $100 prizes will have an outcome of less prizes in total. 

The answer would come out to

48 prizes of $25 each ($1200) 
15 prizes of $100 each ($1500)

which adds to the full amount of $2700 with 63 prizes.