Hard problem, can't get to the right exact answer. (ASAP!)

Question

Uma has $100 and she has to buy 100 balls. A football costs $15, a cricket ball costs $1 and a table-tennis ball costs $0,25. Uma spends the whole amount on buying the 100 balls. How many balls of each type does she buy?

There must be 100 balls and,

an equal $100 must be used too. It has to be exact.

Hint: It is a trial and error question.

Answer 1

15F +C + T/4 = 100 where F = number of Footballs, C = number of Cricket balls, and T =number of Table Tennis balls, where $15 is the cost of one Football, $1 is the cost of one Cricket ball and 1/4 dollar = $0.25 = cost of one Table Tennis ball

F + C + T = 100 = total balls purchased

F,C, and T are integers, not fractions, which eliminates an infinite number of possibilities, narrowing it down to a surprisingly few, when an integer solution is required

3 Footballs, 41 Cricket balls, 56 Tennis balls, sum to 100 balls

$15(3) + $1(41) + $0.25(56) = $45+$41+$14 = $100

or another solution

zero footballs, zero tennis balls and 100 cricket balls

F+C + T = 100

0 + 100 + 0 = 100

$15F + $1C + $0.25T = 100

$15(0) + $1(100) + $0.25(0) = $100