Cum se rezolva problemele:
1. Suma a doua number este 235,iar raportul lor este fractia 2 pe 3. Care sunt numerele?
2. Suma a tree numerele este 403.Al doilea numar este fractia 2 pe 3 din primul,iar al treilea este fractia 3 pe 4 din al doilea.Care sunt numerele?
Va rog ajutatima!Am nevoie de ajutor!!!

[tex]1)a,b-nr.[/tex]

[tex]a + b = 235[/tex]

[tex] \frac{a}{b} = \frac{2}{3} [/tex]

[tex]3a = 2b[/tex]

[tex]a = \frac{2b}{3} [/tex]

[tex] \frac{2b}{3} + b = 235 \: | \times 3[/tex]

[tex]2b + 3b = 705[/tex]

[tex]5b = 705[/tex]

[tex]b = \frac{705}{5} [/tex]

[tex]b = 141[/tex]

[tex]a = \frac{2b}{3} [/tex]

[tex]a = \frac{2 \times 141}{3} [/tex]

[tex]a = \frac{282}{3} [/tex]

[tex]a = 94[/tex]

[tex]2)a,b,c-nr.[/tex]

[tex]a + b + c = 403[/tex]

[tex]b = \frac{2}{3} \times a[/tex]

[tex]b = \frac{2a}{3} [/tex]

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

[tex]c = \frac{3}{4} \times \frac{2a}{3} [/tex]

[tex]c = \frac{2a}{4} [/tex]

[tex]c = \frac{a}{2} [/tex]

[tex]a + \frac{2a}{3} + \frac{a}{2} = 403 \: | \times 6[/tex]

[tex]6a + 4a + 3a = 2418[/tex]

[tex]13a = 2418[/tex]

[tex]a = \frac{2418}{13} [/tex]

[tex]a = 186[/tex]

[tex]b = \frac{2a}{3} [/tex]

[tex]b = \frac{2 \times 186}{3} [/tex]

[tex]b = \frac{372}{3} [/tex]

[tex]b = 124[/tex]

[tex]c = \frac{a}{2} [/tex]

[tex]c = \frac{186}{2} [/tex]

[tex]c = 93[/tex]

[tex]1. \: \: x + y = 235 \\ \frac{x}{y} = \frac{2}{3} = k = > x = 2k \: \: \: y = 3k \\ 2k + 3k = 235 \\ 5k = 235 \\ k = 47 \\ x = 2k = 2 \times 47 = 94 \\ y = 3k = 3 \times 47 = 141[/tex]

[tex]x + y + z = 403 \\ y = \frac{2}{3}x \\ z = \frac{3}{4} y = \frac{3}{4} \times \frac{2}{3} x = \frac{2}{4} x = \frac{1}{2} x \\ x + \frac{2}{3} x + \frac{1}{2} x = 403 \\ amplificam \: fractia \: \frac{2}{3} x \: cu \: 2 \: si \: fractia \\ \frac{1}{2} x \: cu \: 3 \\ x + \frac{4x}{6} + \frac{3x}{6} = 403 | \times 6 \\ 6x + 4x + 3x = 2418 \\ 13x = 2418 \\ x = 186 \\ y = \frac{2}{3} x = \frac{2 \times 186}{3} = \frac{372}{3} = 124 \\ z = \frac{1}{2} x = \frac{186}{2} = 93[/tex]
coroana?