Question

Suma a patru numere 345. aflaţi numerele , ştiind că al doilea este 4/5 din primul, al treilea este 3/4 don al doilea, iar al patrulea este 3/5 din al treilea

Answer 1

Cele patru numere vor fi a, b, c, d. Deci:
[tex]a+b+c+d=345 \\ b=\frac{4}{5}*a\\ c=\frac{3}{4}*b=\frac{3}{4}*\frac{4}{5}*a=\frac{3}{5}*a\\ d=\frac{3}{5}*c=\frac{3}{5}*\frac{3}{5}*a=\frac{9}{25}*a\\ \rightarrow a+\frac{4}{5}*a+\frac{3}{5}*a+\frac{9}{25}*a=345\\ a*(1+\frac{4}{5}+\frac{3}{5}+\frac{9}{25})=345\\ a*\frac{25+20+15+9}{25}=345\\ a*\frac{69}{25}=345\\ a=\frac{345}{69}*25\\ a=5*25\\ a=125\\ \rightarrow b=\frac{4}{5}*a=\frac{4}{5}*125=4*25=100\\ \rightarrow c=\frac{3}{5}*a=\frac{3}{5}*125=3*25=75\\[/tex]
[tex] \rightarrow d=\frac{9}{25}*a=\frac{9}{25}*125=9*5=45\\ Verificare: 125+100+75+45=345[/tex]

Answer 2

a+b+c+d=345
b=4a/5
c=3/4x4a/5=12a/20=3a/5
d=3/5x3a/5=9a/25
a+4a/5+3a/5+9a/25=345
25a+20a+15a+9a=8625
69a=8625
a=125
b=4a/5=500/5=100
c=3a/5=375/5=75
d=9a/25=9x125/25=9x5=45
verificare
125+100+75+45=345