Đáp án:
Giải thích các bước giải:
Gọi số gà trống, mái, con người đó mua được là a,b,c,(a,b,c∈N)a,b,c,(a,b,c∈N)
Theo bài ta có:
⎧⎪ ⎪⎨⎪ ⎪⎩50a+30b+10c3=1000a+b+c=100a≤b≤c{50a+30b+10c3=1000a+b+c=100a≤b≤c
⎧⎨⎩150a+90b+10c=3000a+b+c=100a≤b≤c{150a+90b+10c=3000a+b+c=100a≤b≤c
⎧⎨⎩140a+80b+10(a+b+c)=3000a+b+c=100a≤b≤c{140a+80b+10(a+b+c)=3000a+b+c=100a≤b≤c
⎧⎨⎩140a+80b+10.100=3000a+b+c=100a≤b≤c{140a+80b+10.100=3000a+b+c=100a≤b≤c
⎧⎨⎩140a+80b=2000a+b+c=100a≤b≤c{140a+80b=2000a+b+c=100a≤b≤c
⎧⎨⎩7a+4b=100a+b+c=100a≤b≤c{7a+4b=100a+b+c=100a≤b≤c
Mà a≤b→11a≤7a+4b≤11ba≤b→11a≤7a+4b≤11b
→11a≤100≤11b→11a≤100≤11b
→{a≤9b≥10→{a≤9b≥10
Lại có: 7a+4b=1007a+4b=100
→a⋮4→a=4k→k≤2→a⋮4→a=4k→k≤2
→7.4k+4b=100→b=25−7k→7.4k+4b=100→b=25−7k
→a+b+c=4k+25−7k+c=25−3k+c=100→a+b+c=4k+25−7k+c=25−3k+c=100
→c=75+3k→c=75+3k
→(a,b,c)=(4k,25−7k,75+3k)→(a,b,c)=(4k,25−7k,75+3k)
Mà k≤2→k=0,1,2k≤2→k=0,1,2
+)k=0→(a,b,c)=(0,25,75)+)k=0→(a,b,c)=(0,25,75)
+)k=1→(a,b,c)=(4,18,78)+)k=1→(a,b,c)=(4,18,78)
+)k=2→(a,b,c)=(8,11,81)
