Question

Determinati 5 numere impare consecutive, stiind ca, daca din suma lor scadem suma numerelor pare ce se afla intre ele vom obtine 35.

Answer 1

fie x primul numar impar; celelalte vor fi x+2, x+4, x+6, x+8
numerele pare dintre ele sunt x+1, x+3, x+5, x+7;
 calculam suma numerelor impare:
x+x+2+x+4+x+6+x+8= 5x +20
  calculam suma numerelor pare:
x+1+x+3+x+5+x+7= 4x+ 16
   obtinem ecuatia: 
5x+20 - (4x+16)= 35 
5x+20-4x-16=35
x+4=35
x=31
numerele sunt: 31, 33, 35, 37, 39

Answer 2

b=a+2;
c=a+4;
d=a+6;
e=a+8;
[a+b+c+d+e]-[a+1+a+3+a+5+a+7]=35
⇒[a+a+2+a+4+a+6+a+8]-[4a+1+3+5+7]=35
⇒[5a+2+4+6+8]-[4a+[7·8/2-2+4+6]=35
⇒[5a+2[1+2+3+4]-[4a+[7·4-12]=35
⇒[5a+2[4·5/2]-[4a+[28-12]=35
⇒[5a+2·[2·5]-[4a+16]=35
⇒[5a+2·10]-[4a+16]=35
⇒[5a+20]-[4a+16]=35
⇒[5a-4a]+[20-16]=35
⇒a+4=35
⇒a=35-4
⇒a=31;
⇒b=a+2
⇒b=31+2⇒b=33;
⇒c=a+4
⇒c=31+4⇒c=35;
⇒d=a+6
⇒d=31+6⇒d=37;
⇒e=a+8
⇒e=31+8⇒e=39;