现有1分,2分,5分硬币共100枚,总共价值2元,已知2分硬币总值比1分硬币总值多13分,三类硬币各几枚? _ .

问题描述:

现有1分,2分,5分硬币共100枚,总共价值2元,已知2分硬币总值比1分硬币总值多13分,三类硬币各几枚? ___ .

2元=200分
设1分硬币有x枚,则2分硬币有(x+13)÷2枚,5分硬币的枚数是100-x-(x+13)÷2,根据题意得
x+2×[(x+13)÷2]+5×[100-x-(x+13)÷2]=200
                    x+x+13+500-7.5x-32.5=200
                              480.5-5.5x=200
                               480.5-200=5.5x
                                   280.5=5.5x
                                       x=51
(x+13)÷2=(51+13)÷2=32
100-51-32=17(枚)
答:1分硬币51枚,2分硬币32枚,5分硬币17枚.