Question

trei numere naturale de 2 cifre sunt direct proportionale cu numerele 5,(3), 3,75, 1,(6). Determinati suma numerelor

Answer 1

5(3)=1 intreg si 5pe 9
3,75=375supra 100
1(6)=1intreg si 6supra9
14 pe 9 + 375 pe 100 +15 pe 9
aducem la acelasi numitor si obtinem 6275supra 900 adica 6,97

Answer 2

{a, b, c} D.P. {5,(3), 3,75, 1,(6)}

$\frac{a}{ \frac{53-5}{9} }= \frac{b}{ \frac{375\div25}{100\div25} }=\frac{c}{\frac{16-1}{9}} }$

$a\cdot \frac{9}{48}=b\cdot \frac{4}{15}=c\cdot \frac{3}{5}=k$

⇒ $a=k\cdot \frac{16}{3} , b=k \cdot \frac {15}{4} , c= \cdot \frac{5}{3}$


$a+b+c=\frac{16k}{3}+\frac{15k}{4}+\frac {5k}{3}$

$a+b+c=\frac {16k\cdot4+15k\cdot3+5k\cdot4}{3\cdot4}$

$a+b+c=\frac{64k+45k+20k}{12}$

$a+b+c=\frac{129}{12}$

$\boxed{\boxed{a+b+c=\frac{43}{4}}}$