Question

sa se determine trei numere proportionale cu 5 ,7 si 10 a caror medie aritmetica este 22

Answer 1

[tex]\{a,b,c\}d.p.\{5,7,10\}\Rightarrow \frac{a}{5}=\frac{b}{7}=\frac{c}{10}=k \Rightarrow a=5k,\\ b=7k, c=10 k\\ \frac{a+b+c}{3}=22\\ a+b+c=66\\ 5k+7k+10k=66\\ 22k=66 \Rightarrow k=3\\ a=5k=\boxed{15}\\ b=7k=\boxed{21}\\ c=10k=\boxed{30}\\[/tex]

Answer 2

Ma=(a+b+c)/3=22
x/5=y/7=z/10=k
x=5k
y=7k
z=10k

a+b+c=22*3
5k+7k+10k=66
22k=66
k=3            x=5*3=15
                   y=7*3=21
                   z=10*3=30