[tex]\frac{20\%\cdot a}{\frac{1}{2}}=\frac{25\%\cdot b}{\frac{35}{48}}=\frac{30\%\cdot c}{1}[/tex]
[tex]\frac{\frac{20a}{100}}{\frac{1}{2}}=\frac{\frac{25b}{100}}{\frac{35}{48}}=\frac{30c}{100}[/tex]
[tex]\frac{\frac{a}{5}}{\frac{1}{2}}=\frac{\frac{b}{4}}{\frac{35}{48}}=\frac{3c}{10}[/tex]
[tex]\frac{\frac{2a}{5}}{1}=\frac{\frac{48b}{4}}{35}=\frac{3c}{10}[/tex]
[tex]\frac{2a}{5}=\frac{12b}{35}=\frac{3c}{10}[/tex]
Fie toate fractiile egale cu k, atunci
2a=5k, 12b=35k, 3c=10k
[tex]a=\frac{5k}{2}, b=\frac{35k}{12}, c=\frac{10k}{3}[/tex]
a+b+c=21
[tex]\frac{5k}{2}+\frac{35k}{12}+\frac{10k}{3}=21[/tex]
[tex]\frac{30k}{12}+\frac{35k}{12}+\frac{40k}{12}=21[/tex]
[tex]\frac{105k}{12}=21[/tex]
[tex]105k=252[/tex]
[tex]k=\frac{252}{105}=\frac{84}{35}=\frac{12}{5}[/tex]
[tex]a=\frac{5\cdot\frac{12}{5}}{2}=\frac{12}{2}=6[/tex]
[tex]b=\frac{35\cdot\frac{12}{5}}{12}=\frac{7\cdot12}{12}=7[/tex]
[tex]c=\frac{10\cdot{12}{5}}{3}=\frac{2\cdot12}{3}=\frac{24}{3}=8[/tex]
a=6, b=7, c=8
