Question

已知正整数a.b.c.d满足条件a/b=b/c=c/d=5/8,且a+b++c+d=1157,求a+b+c-d的值

Answer 1

正整数a.b.c.d满足条件a/b=b/c=c/d=5/8,a= 5/8b,b=5/8c,c=5/8d,a:b:c:d=1:(5/8):(5/8 * 5/8):(5/8*5/8*5/8)=512:320:200:125,设a=512k,b=320k,c=200k,d=125k ,且a+b++c+d=1157,512k+320k+200k0125k=1157,k=1.a+b+c-d=512+320+200-125=907.

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