Odpowiedź :
1.
x - licznik
y - iloraz szukanego ułamka
[tex]\frac{x}{y+0,5x} = \frac{5}{21}\\\frac{x+8}{y+8} = \frac{2}{5}\\\\21x=5(y+0,5x)\\5(x+8) = 2(y + 8)\\\\21x = 5y + 2,5x\\5x+40 = 2y+16\\\\21x - 2,5x -5y = 0\\5x-2y = 16-40\\\\18,5x - 5y = 0 \ \ /\cdot2\\ 5x-2=-24 \ \ /\cdot(-5)\\\\37x-10y = 0\\-25x+10y = 120\\--------- \ \ \ +\\12x = 120 \ \ /:12\\\underline{x = 10}\\\\2y = 5x+24 = 5\cdot10+24 = 50+24 = 74\\2y = 74 \ \ /:2\\\underline{y = 37}\\\\Odp. \ Ten \ ulamek \ to \ \frac{10}{37}\\\\\\Spr.[/tex]
[tex]\frac{x}{y+0,5x} = \frac{10}{37+5} = \frac{10}{42} = \frac{5}{21}\\\\\frac{x+8}{y+8} = \frac{10+8}{37+8} = \frac{18}{45} = \frac{2}{5}[/tex]
2.
x - wiek babci
y - wiek wnuczki
[tex]x = 48+y\\x-5 = 13(y-5)\\\\x-y = 48 \\x-5 = 13y - 65\\\\x-y = 48 \ \ /\cdot(-13)\\x-13y = -60\\\\-13x + 13y = -624\\x -13y = -60\\----------- \ \ +\\-12x= -684 \ \ /:(-12)\\\underline{x = 57 \ lat}\\\\y = x-48 = 57-48\\\underline{y = 9 \ lat}[/tex]
Odp. Babcia ma 57 lat, a wnuczka 9.