Răspuns :
1.Fie a, b, c cele 3 numere
b = 40 + a/2
c = 3*a
a + b + c = 1012
a + ( 40 + a/2 ) + 3*a = 1012
a + 40 + a/2 + 3*a = 1012
a + 3*a + a/2 = 1012 - 40
4*a + a/2 = 972
( aducem la acelasi numitor (comun) si apoi inmultim totul cu 2 ca sa scapam de fractie)
2*4*a + a = 972*2
8*a + a = 1944
9*a = 1944
a = 1944/9
a = 216
b = 40 + a/2 = 40 + 108 = 148
c = 3*a = 3*216 = 648
VERIFICARE : a + b + c = 216 + 148 + 648 = 1012 CORECT
2.
1.a+b+c=710
b=2a+15
c=3b-25
c=3(2a+15)-25⇒ c=6a+45-25
c=6a+20
a+2a+15+6a+20=710
9a=710-15-20
9a=675
a=675/9
a=75
b=2·75+15
b=165
c=6·75+20
c=470
verificare
75+165+470+710a+b=429
a-2b=114
rezolvare:
2.a+b=429
a=429-b
inlocuim in a-2b=114
429-b-2b=114
429-3b=114
3b=429-114
3b=315
b=315/3
b=105
a+b=429
a=429-105
a=324
3.
a+b=429
b-2a=114
a=429-b
b-2(429-b)=114
3b=972
b=324
a+324=429
a=105
b = 40 + a/2
c = 3*a
a + b + c = 1012
a + ( 40 + a/2 ) + 3*a = 1012
a + 40 + a/2 + 3*a = 1012
a + 3*a + a/2 = 1012 - 40
4*a + a/2 = 972
( aducem la acelasi numitor (comun) si apoi inmultim totul cu 2 ca sa scapam de fractie)
2*4*a + a = 972*2
8*a + a = 1944
9*a = 1944
a = 1944/9
a = 216
b = 40 + a/2 = 40 + 108 = 148
c = 3*a = 3*216 = 648
VERIFICARE : a + b + c = 216 + 148 + 648 = 1012 CORECT
2.
1.a+b+c=710
b=2a+15
c=3b-25
c=3(2a+15)-25⇒ c=6a+45-25
c=6a+20
a+2a+15+6a+20=710
9a=710-15-20
9a=675
a=675/9
a=75
b=2·75+15
b=165
c=6·75+20
c=470
verificare
75+165+470+710a+b=429
a-2b=114
rezolvare:
2.a+b=429
a=429-b
inlocuim in a-2b=114
429-b-2b=114
429-3b=114
3b=429-114
3b=315
b=315/3
b=105
a+b=429
a=429-105
a=324
3.
a+b=429
b-2a=114
a=429-b
b-2(429-b)=114
3b=972
b=324
a+324=429
a=105