a) [tex] \frac{x}{y} = \frac{2}{7} [/tex]
si y-x=50, adica
y=x+50
Folosim proprietatile proportiilor:
[tex] \frac{x}{y-x} = \frac{2}{7-2} [/tex]
[tex] \frac{x}{50} = \frac{2}{5} [/tex]
x=[tex] \frac{2*50}{5} [/tex]
x=20
y=20+50=70
b)1) [tex] \frac{x}{3} = \frac{5}{1} [/tex]
x=3*5=15
2) 0,(3)=[tex] \frac{3}{9} [/tex]=[tex] \frac{1}{3} [/tex]
0,(2)=[tex] \frac{2}{9} [/tex] deci:
[tex] \frac{0,(3)}{x} = \frac{2}{0,(2)} [/tex] este echivalent cu:
[tex] \frac{ \frac{1}{3} }{x} = \frac{2}{ \frac{2}{9} } [/tex] adica:
[tex] \frac{1}{3x} [/tex]=[tex] \frac{9}{1} [/tex] de unde:
x=[tex] \frac{1}{27} [/tex]
3) Daca ecuatia corecta este:
[tex] \frac{x}{0,5} = \frac{1}{ \frac{2}{3} } [/tex] atunci avem:
[tex] \frac{x}{ \frac{5}{10} } = \frac{3}{2} [/tex], adica:
[tex] \frac{x}{ \frac{1}{2} } = \frac{3}{2} [/tex] care inseamna:
[tex] \frac{2x}{1} = \frac{3}{2} [/tex], deci:
x=[tex] \frac{3}{4} [/tex]
sau: Daca ecuatia este:
[tex] \frac{x}{0,5} = \frac{ \frac{1}{2} }{3} [/tex] atunci avem:
[tex] \frac{x}{ \frac{1}{2} } = \frac{1}{6} [/tex] care inseamna:
[tex] \frac{2x}{1} = \frac{1}{6} [/tex], deci:
x=[tex] \frac{1}{12} [/tex]
