{a, b, c} D.P. {5,(3), 3,75, 1,(6)}
[tex] \frac{a}{ \frac{53-5}{9} }= \frac{b}{ \frac{375\div25}{100\div25} }=\frac{c}{\frac{16-1}{9}} } [/tex]
[tex]a\cdot \frac{9}{48}=b\cdot \frac{4}{15}=c\cdot \frac{3}{5}=k [/tex]
⇒ [tex]a=k\cdot \frac{16}{3} , b=k \cdot \frac {15}{4} , c= \cdot \frac{5}{3}[/tex]
[tex] a+b+c=\frac{16k}{3}+\frac{15k}{4}+\frac {5k}{3}[/tex]
[tex]a+b+c=\frac {16k\cdot4+15k\cdot3+5k\cdot4}{3\cdot4}[/tex]
[tex]a+b+c=\frac{64k+45k+20k}{12}[/tex]
[tex]a+b+c=\frac{129}{12}[/tex]
[tex]\boxed{\boxed{a+b+c=\frac{43}{4}}}[/tex]
