Question

Trei numere sunt invers proportionale cu numerele 1/4,1/5 si 1/7. Aflati numerele stiind ca diferenta dintre cel mai mare numar si cel mai mic este 45.

Answer 1

[tex]Notam\ numerele\ cu\ a,b\ si\ c:\\ (a,b,c) i.p.(\frac{1}{4},\frac{1}{5},\frac{1}{7})\Rightarrow\frac{ \frac{a}{1}}{\frac{1}{4}}=\frac{ \frac{b}{1}}{\frac{1}{5}}=\frac{ \frac{c}{1}}{\frac{1}{7}}\Rightarrow \frac{a}{4}=\frac{b}{5}=\frac{c}{7}=k\Rightarrow a=4k,b=5k\\ c=7k\\ Stim\ ca:\\ c-a=45\\ 7k-4k=45\\ 3k=45\Rightarrow \bold{k=15}\\ a=4k\Rightarrow \bold{a=60}\\ b=5k\Rightarrow \bold{b=75}\\ c=7k\Rightarrow \bold{c=105}\\ R:Numerele\ cautate\ sunt\ 60,75\ si\ 105.[/tex]