Răspuns:
{a,b,c} direct proportionale cu {1/12,1/10,1/6} =>
a/(1/12) = b/(1/10) = c/(1/6) = k
a = k/12
b = k/10
c = k/6
a + b + c = 7
⁵⁾k/12 + ⁶⁾k/10 + ¹⁰⁾k/6 = ⁶⁰⁾7
5k + 6k + 10k = 420
21k = 420
k = 20
a = 20/12 = 5/3
b = 20/10 = 2
c = 20/6 = 10/3
Verificare :
5/3 + ³⁾2 + 10/3 =
= (5 + 6 + 10)/3
= 21/3
= 7