Respuesta :
Answer :
- 81 : 68
⠀
Step-by-step explanation:
⠀
[tex] {\longrightarrow \: \sf \: Let \: \: a : b\: = 3: 4 = \dfrac{a}{b} \: = \: \dfrac{3}{4} = k}[/tex]
⠀
Therefore,
⠀
[tex] \dashrightarrow \qquad \sf \: a = 3k[/tex]
[tex] \dashrightarrow \qquad \sf \: b = 4k[/tex]
⠀
Now, Substituting the values :
⠀
[tex]\longrightarrow \qquad \sf \: 15a+9b:16a+5b[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{15(3k)+9(4k)}{16(3k)+5(4k)}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{45k+36k}{48k+20k}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81k}{68k}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81 \cancel{k}}{68 \cancel{k}}[/tex]
⠀
[tex]\longrightarrow \qquad \sf \: \dfrac{81}{68}[/tex]
⠀
[tex]\longrightarrow \qquad \bf \: {81} : {68}[/tex]
⠀
Therefore ,
⠀
[tex]{ \pmb{ \sf{\longrightarrow \qquad \: 15a+9b:16a+5b = 81 : 68}}}[/tex]
⠀
