Question

patru nr naturale au suma 100 daca din primul scad 6 la al doilea adun 8 la al treilea adun 5 din al patrulea scad 7 si obtin patru nr naturale pare consecutive
Care sunt nr

Answer 1

a+b+c+d=100
(a-6)+(b+8)+(c+5)+(d-7)=4 nr.pare consecutive.
-------------------------------------------------------------
a=?b=?c=?d=?

a+b+c+d+(8+5)-(6+7)=100
a+b+c+d+13-13=100----------=> cele 4 nr.consecutive =100

Aflam cele 4 numere pare.

a+b+c+d=a+a+2+a+4+a+6.....=>
a+b+c+d=4a+12
100=4a+12

4a=100-12
4a=88
a=88:4
a=22

b=22+2...=>b=24
c=22+4...=>c=26
d=22+6...=>d=28

=> cele 4 numere pare consecutive sunt: 22, 24, 26, si 28

Aflam numerele initiale.

a=22+6...=>a=28
b=24-8...=>b=16
c=26-5...=>c=21
d=28+7..=>d=35

=> numerele initiale sunt:  28, 16, 21 si 35

si avem.....

28+16+21+35=
=44+56
=100

(28-6)+(16+8)+(21+5)+(35-7)=
=22+24+26+28 (cele 4 nr.consecutive)
=46+54
=100

=>100=100