解:設(shè)??????$?1?$??????角、??????$?5?$??????角、??????$?1?$??????元的硬幣各取了??????$?x?$??????枚、??????$?y?$??????枚、??????$?z?$??????枚
根據(jù)題意,得
??????$? {{\begin{cases} { {x+y+z=15,①}} \\{0.1x+0.5y+z=7,②}\end{cases}}}?$??????
??????$? ②×10-①,?$??????得
??????$? z=\frac {55-4y}9?$??????
因?yàn)??????$?y,?$????????????$?z?$??????都為整數(shù),則??????$?y=7,?$????????????$?z=3?$??????
把??????$?y=7,?$????????????$?z=3?$??????代入①,得??????$?x=5?$??????
所以方程組的解為??????$?{{\begin{cases} { {x=5}} \\{y=7} \\{z=3} \end{cases}}}?$??????
答:??????$?1?$??????角、??????$?5?$??????角、??????$?1?$??????元的硬幣各取了??????$?5?$??????枚、??????$?7?$??????枚、??????$?3?$??????枚