Suma a 4 numere este 482 . Aflati numerele , stiind ca primul reprezinta 80% din al doilea , al doilea 75% din al treilea , si al treilea reprezinta 60% din al patrulea .

[tex]a,b,c,d-nr.[/tex]

[tex]a + b + c + d = 482[/tex]

[tex]a = \frac{80}{100} \times b = \frac{8b}{10} = \frac{4b}{5} [/tex]

[tex]b = \frac{75}{100} \times c = \frac{3c}{4} [/tex]

[tex]c = \frac{60}{100} \times d = \frac{6d}{10} = \frac{3d}{5} [/tex]

[tex]a = \frac{4b}{5} = \frac{4 \times \frac{3c}{4} }{5} = \frac{3c}{5} [/tex]

[tex]c = \frac{3d}{5} [/tex]

[tex]5c = 3d[/tex]

[tex]d = \frac{5c}{3} [/tex]

[tex] \frac{3c}{5} + \frac{3c}{4} + c + \frac{5c}{3} = 482[/tex]

[tex] \frac{36c}{60} + \frac{45c}{60} + \frac{60c}{60} + \frac{100c}{60} = \frac{28920}{60}[/tex]

[tex]36c + 45c + 60c + 100c = 28920[/tex]

[tex]241c = 28920[/tex]

[tex]c = \frac{28920}{241} [/tex]

[tex]c = 120[/tex]

[tex]a = \frac{3c}{5} = \frac{3 \times 120}{5} = \frac{360}{5} = 72[/tex]

[tex]b = \frac{3c}{4} = \frac{3 \times 120}{4} = \frac{360}{4} = 90[/tex]

[tex]d = \frac{5c}{3} = \frac{5 \times 120}{3} = \frac{600}{3} = 200[/tex]