lets assume that it is possible to change $15 into an equal number of half-dollars, quarters, and dimes

let x = the equal number of half-dollars, quarters, and dimes, where x is integer, x>0

then

0.50x + 0.25x + 0.10x = 15

x = 17.65

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since the solution of the equation is not an integer follows there is no such integer x thus it is not possible to change $15 into an equal number of half-dollars, quarters, and dimes.