A word problem

Question

The money that Aileen had was a whole number. She wished to buy a guitar but was short of $110.70. Bob wanted to purchase the same guitar using all his money but was short of $2.50. If they pooled their money together, the sum was still insufficient to buy the guitar. Find the price of the guitar.

Answer 1

Aileen has less than $2.50 (other wise she could make up for Bob's shortage). Yet her amount is a whole number. So she has only $2.00 (at most). So the guitar costs at least $112.70.