a - creioane, b - caiete, c - penare, d - carti
a+c=b+d+10000, a=b+d-c+1000
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[tex]b= \frac{2}{4}(a+c+d) [/tex]
[tex]c= \frac{4}{17}(a+b+d) [/tex]
[tex]d= \frac{1}{20}(a+b+c) [/tex]
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il inlocuim pe a in cele 3 relatii
[tex]b= \frac{2}{4}(b+d-c+10000)+ \frac{2}{4}c + \frac{2}{4}d [/tex]
[tex]b= \frac{2}{4}b+d+5000 [/tex]
[tex] \frac{2}{4}b=d+5000 [/tex]
[tex]b=2d+10000[/tex]
[tex]c= \frac{4}{17}(b+d-c+10000)+ \frac{4}{17}b+ \frac{4}{17}d [/tex]
[tex]c= \frac{8}{17}d+ \frac{8}{17}b- \frac{4}{17}c+ \frac{40000}{17} [/tex]
[tex] \frac{21}{17}c= \frac{8}{17}b+ \frac{8}{17}d+ \frac{40000}{17} [/tex]
[tex] \frac{21}{17}c = \frac{8}{17}(2d+10000)+ \frac{8}{17}d + \frac{40000}{17} [/tex]
[tex] \frac{21}{17}c= \frac{16}{17}d+ \frac{80000}{17}+ \frac{8}{17}d+ \frac{40000}{17} [/tex]
[tex]21c=24d+120000[/tex]
[tex]c= \frac{24d+120000}{21} [/tex]
[tex]d= \frac{1}{20}(b+d-c+10000)+ \frac{1}{20}b+ \frac{1}{20}c [/tex]
[tex]d= \frac{2}{20}b+ \frac{1}{20}d+500 [/tex]
[tex]d= \frac{2}{20}(2d+10000)+ \frac{1}{20}d+500 [/tex]
[tex]d= \frac{4}{20}d+ \frac{20000}{20}+ \frac{1}{20}d+500 [/tex]
[tex]20d=4d+20000+d+10000[/tex]
[tex]15d=30000[/tex]
[tex]d=30000:15[/tex]
[tex]d=2000 [/tex] numarul cartilor
[tex]b=2*2000+10000[/tex]
[tex]b=14000[/tex] numarul caietelor
[tex]c= \frac{24*2000+120000}{21} [/tex]
[tex]c=8000[/tex] numarul penarelor
[tex]a=14000+2000-8000+10000[/tex]
[tex]a=18000[/tex] numarul creioanelor
