Question

problema 4 urgent dau coronita si 20 puncte

Answer 1

$a + b + c + d = 375$

$100 \% - 20 \% = 80 \%$

$\frac{80}{100} \times a = \frac{8a}{10} = \frac{4a}{5} (restul \: primului \: elev)$

$100 \% - 40 \% = 60 \%$

$\frac{60}{100} \times b = \frac{3b}{5} (restul \: celui \: de - al \: doilea \: elev)$

$100 \% - 25 \% = 75 \%$

$\frac{75}{100} \times c = \frac{3c}{4} (restul \: celui \: de - al \: treilea \: elev)$

$100 \% - 50 \% = 50 \%$

$\frac{50}{100} \times d = \frac{d}{2} (restul \: celui \: de - al \: patrulea \: elev)$

$\frac{4a}{5} = \frac{ 3b}{5} = \frac{3c}{4} = \frac{d}{2}$

$\frac{4a}{5} = \frac{3b}{5} = > 4a = 3b = > b = \frac{4a}{3}$

$\frac{3b}{5} = \frac{3c}{4}$

$\frac{3 \times \frac{4a}{3} }{5} = \frac{3c}{4}$

$\frac{4a}{5} = \frac{3c}{4}$

$4a \times 4 = 3c \times 5$

$16a = 15c = > c = \frac{16a}{15}$

$\frac{3c}{4} = \frac{d}{2}$

$\frac{3 \times \frac{16a}{15} }{4} = \frac{d}{2}$

$\frac{ \frac{16a}{5} }{4} = \frac{d}{2}$

$\frac{16a}{5} \times \frac{1}{4} = \frac{d}{2}$

$\frac{4a}{5} = \frac{d}{2}$

$4a \times 2 = 5d$

$8a = 5d = > d = \frac{8a}{5}$

$a + b + c + d = 375$

$a + \frac{4a}{3} + \frac{16a}{15} + \frac{8a}{5} = 375 \: | \times 15$

$15a + 20a + 16a + 24a = 5625$

$75a = 5625 \: | \div 75$

$a = 75$

$b = \frac{4a}{3} = \frac{4 \times 75}{3} = 4 \times 25 = 100$

$c = \frac{16a}{15} = \frac{16 \times 75}{15} = 16 \times 5 = 80$

$d = \frac{8a}{5} = \frac{8 \times 75}{5} = 8 \times 15 = 120$