i am not sure how one on a "poor limited budget" would be able to make that many quilts (fabric, batting, binding, quilting or tying) in the time frame given. my 2012 quilting goal was to get one quilt completed every month so i can not imagine 115. perhaps the goal needs to be reassessed and look at what can be accomplished with the budget and any donations received. i would say on the small end a lap quilt size would be 45" x 60" up to 60" x 72".
there are many simple quilt patterns available free by doing an internet search. for quilt backs and batting, you can search the thrift stores for blankets to use for batting and sheets to use for quilt backs also used clothing that you can use for quilt pieces. does the 22 year old have others to help her make quilts? hopefully she has plenty of help. good luck on this journey.