Question

a+b+c=3113
a:(b:2)=3 rest 5
c:(b:4)=5 rest 3
a;b;c=?

Answer 1

a + b + c = 3 113
a : (b:2) = 3 rest 5 ==>
==> a = 3×b:2 + 5 |×2
==> 2×a = 3×b + 10
==> a = (3×b+10) : 2

c : (b:4) = 5 rest 3 ==>
==> c = 5×b:4 + 3 |×4
==> 4×c = 5×b + 12
==> c = (5×b+12) : 4

inlocuim in prima relatie in functie de b
(3×b+10) : 2 + b + (5×b+12) : 4 = 3 113 |×4
2×(3×b+10) + 4×b + 5×b + 12 = 12 452
6×b + 20 + 9×b = 12 452 - 12
15 × b = 12 440 - 20
15 × b = 12 420 |:15
b = 828

a = (3×828+10) : 2 = 2 494 : 2 = 1 247

c = (5×828 + 12) : 4 = 4 152 : 4 = 1 038

a = 1 247
b = 828
c = 1 038

Verificare:
1 247 + 828 + 1 038 = 3 113