Răspuns: a = 99; b = 100; c = 101
Explicație pas cu pas:
3 a + 2 b + c = 598
a + 2 b + 3 c= 602
________________ adun relatiile
4 a + 4 b + 4 c = 1200
4 × ( a + b + c ) = 1 200
a + b + c = 1 200 : 4
a + b + c = 300 → suma celor trei numere naturale
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a + 2 b + 3 c = 602
3 a + 2 b + c = 598
__________________ scad relatiile
- 2 a + 2 c = 602 - 598
2 c - 2 a = 4
2 × ( c - a ) = 4 [ : 2
c - a = 2 ⇒ c = a + 2
a < b < c ⇒ b > a cu 1 ⇒ a, b, c sunt numere consecutive
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a + b + c = 300
a + ( a + 1 ) + ( a + 2 ) = 300
3 × a + 3 = 300
3 × ( a + 1 ) = 300 [ : 3
a + 1 = 100 ( b )
100 - 1 = 99 ( a )
99 + 2 = 101 ( c )
Verific:
a + b + c = 99 + 100 + 101 = 300
a < b < c; 99 < 100 < 101 -> numere consecutive
