[tex]a + b + c + d = 375[/tex]
[tex] 100 \% - 20 \% = 80 \%[/tex]
[tex] \frac{80}{100} \times a = \frac{8a}{10} = \frac{4a}{5} (restul \: primului \: elev)[/tex]
[tex]100 \% - 40 \% = 60 \%[/tex]
[tex] \frac{60}{100} \times b = \frac{3b}{5} (restul \: celui \: de - al \: doilea \: elev)[/tex]
[tex]100 \% - 25 \% = 75 \%[/tex]
[tex] \frac{75}{100} \times c = \frac{3c}{4} (restul \: celui \: de - al \: treilea \: elev)[/tex]
[tex]100 \% - 50 \% = 50 \%[/tex]
[tex] \frac{50}{100} \times d = \frac{d}{2} (restul \: celui \: de - al \: patrulea \: elev)[/tex]
[tex] \frac{4a}{5} = \frac{ 3b}{5} = \frac{3c}{4} = \frac{d}{2} [/tex]
[tex] \frac{4a}{5} = \frac{3b}{5} = > 4a = 3b = > b = \frac{4a}{3} [/tex]
[tex] \frac{3b}{5} = \frac{3c}{4} [/tex]
[tex] \frac{3 \times \frac{4a}{3} }{5} = \frac{3c}{4} [/tex]
[tex] \frac{4a}{5} = \frac{3c}{4} [/tex]
[tex]4a \times 4 = 3c \times 5[/tex]
[tex]16a = 15c = > c = \frac{16a}{15} [/tex]
[tex] \frac{3c}{4} = \frac{d}{2} [/tex]
[tex] \frac{3 \times \frac{16a}{15} }{4} = \frac{d}{2} [/tex]
[tex] \frac{ \frac{16a}{5} }{4} = \frac{d}{2} [/tex]
[tex] \frac{16a}{5} \times \frac{1}{4} = \frac{d}{2} [/tex]
[tex] \frac{4a}{5} = \frac{d}{2} [/tex]
[tex]4a \times 2 = 5d[/tex]
[tex]8a = 5d = > d = \frac{8a}{5} [/tex]
[tex]a + b + c + d = 375[/tex]
[tex]a + \frac{4a}{3} + \frac{16a}{15} + \frac{8a}{5} = 375 \: | \times 15[/tex]
[tex]15a + 20a + 16a + 24a = 5625[/tex]
[tex]75a = 5625 \: | \div 75[/tex]
[tex]a = 75[/tex]
[tex]b = \frac{4a}{3} = \frac{4 \times 75}{3} = 4 \times 25 = 100[/tex]
[tex]c = \frac{16a}{15} = \frac{16 \times 75}{15} = 16 \times 5 = 80[/tex]
[tex]d = \frac{8a}{5} = \frac{8 \times 75}{5} = 8 \times 15 = 120[/tex]
