Question

O tipografie a tiparit in prima saptamana 1/5din nr total al cartilor pe care le avea de tiparit, in a 2 a saptam 1/3 din rest, si in a3 a sapt 1/4din noul rest, iar in a 4 a saptam restul de 1320 de carti. Cate carti s au tiparit in cele 4 saptam ?

Answer 1

in prima saptamana: a/5
in a doua saptamana:1/3(a-a/5)=1/3x4a/5=4a/15
in a treia saptamana: 1/4x(a-a/5-4a/15)=1/4(15a-3a-4a)/15=2a/15
in a patra saptaman:1320

a=a/5+4a/15+2a/15+1320
a=a/5+6a/15+1320
numitor comun 15
15a=3a+6a+1320x15
15a=9a+19800
15a-9a=19800
6a=19800
a=19800:6
a=3300 carti s-au tiparit in cele 4 saptamani