Question

41)La un centru de librarii s-au adus creioane,caiete,penare si carti.Creioanele sunt (fractia) 3 supra 4 din celelalte,caiete (fractia) 2 supra 4,penare (fractia) 4 supra 17 din celelalte,iar carti (fractia) 1 supra 20 din celelalte.Sa se afle cate s-au adus din fiecare,stiind ca penare si creioane s-au adus cu 10000 mai multe decat carti si caiete.Va rog rezolvarea completa!!!UUURRRGGGEEENNNTTT!!!Dau cel mai bun raspuns!!!

Answer 1

a - creioane, b - caiete, c - penare, d - carti
a+c=b+d+10000, a=b+d-c+1000
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$b= \frac{2}{4}(a+c+d)$
$c= \frac{4}{17}(a+b+d)$
$d= \frac{1}{20}(a+b+c)$
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il inlocuim pe a in cele 3 relatii

$b= \frac{2}{4}(b+d-c+10000)+ \frac{2}{4}c + \frac{2}{4}d$
$b= \frac{2}{4}b+d+5000$
$\frac{2}{4}b=d+5000$
$b=2d+10000$

$c= \frac{4}{17}(b+d-c+10000)+ \frac{4}{17}b+ \frac{4}{17}d$
$c= \frac{8}{17}d+ \frac{8}{17}b- \frac{4}{17}c+ \frac{40000}{17}$
$\frac{21}{17}c= \frac{8}{17}b+ \frac{8}{17}d+ \frac{40000}{17}$
$\frac{21}{17}c = \frac{8}{17}(2d+10000)+ \frac{8}{17}d + \frac{40000}{17}$
$\frac{21}{17}c= \frac{16}{17}d+ \frac{80000}{17}+ \frac{8}{17}d+ \frac{40000}{17}$
$21c=24d+120000$
$c= \frac{24d+120000}{21}$

$d= \frac{1}{20}(b+d-c+10000)+ \frac{1}{20}b+ \frac{1}{20}c$
$d= \frac{2}{20}b+ \frac{1}{20}d+500$
$d= \frac{2}{20}(2d+10000)+ \frac{1}{20}d+500$
$d= \frac{4}{20}d+ \frac{20000}{20}+ \frac{1}{20}d+500$
$20d=4d+20000+d+10000$
$15d=30000$
$d=30000:15$
$d=2000$ numarul cartilor

$b=2*2000+10000$
$b=14000$ numarul caietelor

$c= \frac{24*2000+120000}{21}$
$c=8000$ numarul penarelor

$a=14000+2000-8000+10000$
$a=18000$ numarul creioanelor