Question

suma a doua numere este 2490.Sa se afle aceste numere stiind ca 6,5% din primul numar este 8,5% din al doilea numar ?

Answer 1

 

$\displaystyle\\x=\text{primul numar}\\y=\text{al doilea numar}\\\\x+y=2490\\6,5\%\cdot x=8,5\%\cdot y\\.............\\x+y=2490\\\frac{6,5}{100}\cdot x=\frac{8,5}{100}\cdot y~~\Big|\cdot100\\.............\\x+y=2490\\6,5\cdot x=8,5\cdot y~~\Big|\cdot10\\..............\\x+y=2490\\65x=85y~~\Big|~:5\\...............\\x+y=2490~~~~\implies~~y=2490-x\\13x=17y\\..................$

$\displaystyle\\13x=17(2490-x)\\\\13x=17\times2490-17x\\\\13x=  42330-17x\\\\13x+17x=42330\\\\30x=42330\\\\x=42330:30\\\\\boxed{x=1411}\\\\y=4290-x = 4290-1411\\\\\boxed{y=1079}$