notam nepotii cu a, b, c
a + b + c = 85
{a, b, c} i.p. { 7, 9, 12}
7a = 9b = 12c = k
[tex]a = \frac{k}{7} [/tex]
[tex]b = \frac{k}{9} [/tex]
[tex]c = \frac{k}{12} [/tex]
a + b + c = 85
[tex] \frac{k}{7} + \frac{k}{9} + \frac{k}{12} = 85[/tex]
Amplificam și vom obține:
36 k + 28 k + 21 k = 21420
85 k = 21420
k = 252
[tex]a = \frac{252}{7} = 36 \:lei[/tex]
[tex]b = \frac{252}{9} = 28 \: lei[/tex]
[tex]c = \frac{252}{12} = 21 \: lei[/tex]
