Question

Aflati numarul X din egalitatile:
A)X+2•X+3•X+4•X+......+30•X=465;
B)5•X+10•X+15•X+......+150•X=6975.
Dau Coronita

Answer 1

$\displaystyle a).x+2x+3x+4x+...+30x=465 \\ \\ x(1+2+3+4+...+30)=465 \\ \\ x \cdot \frac{30(30+1)}{2} =465 \\ \\ x \cdot \frac{30 \cdot 31}{2} =465 \\ \\ x \cdot \frac{930}{2} =465 \\ \\ 465x=465 \\ \\ x= \frac{465}{465} \\ \\ x=1$

$\displaystyle b).5x+10x+15x+150x=6975 \\ \\ 5x(1+2+3+...+30)=6975 \\ \\ 5x \cdot \frac{30(30+1)}{2} =6975 \\ \\ 5x \cdot \frac{30 \cdot 31}{2} =6975 \\ \\ 5x \cdot \frac{930}{2} =6975 \\ \\ 5x \cdot 465=6975 \\ \\ 2325x=6975 \\ \\ x= \frac{6975}{2325} \\ \\ x=3$