Notăm raportul:
[tex]\dfrac{x}{y} = \dfrac{3}{10} \Rightarrow \dfrac{x}{3} = \dfrac{y}{10} = k \Rightarrow x = 3k, \ y = 10k[/tex]
[tex]a) \ \dfrac{x+y}{y} = \dfrac{3k+10k}{10k} = \dfrac{13k^{(k} }{10k} = \dfrac{13}{10}[/tex]
[tex]b) \ \dfrac{x}{y-x} = \dfrac{3k}{10k-3k} = \dfrac{3k^{(k} }{7k} = \dfrac{3}{7}[/tex]
[tex]c) \ \dfrac{x}{10\cdot y} = \dfrac{3k}{10 \cdot 10k} = \dfrac{3k^{(k} }{100k} = \dfrac{3}{100}[/tex]
[tex]d) \ \dfrac{10\cdot x + 3\cdot y}{9\cdot y} = \dfrac{10\cdot 3k + 3\cdot 10k}{9\cdot 10k} = \dfrac{30k + 30k}{90k} = \dfrac{60k^{(30k} }{90k} = \dfrac{2}{3}[/tex]
