The given problem can be exemplified in the following diagram:
From the line we get the following relationship:
[tex]RS+ST=RT[/tex]Replacing the values:
[tex](8y+2)+(5y+7)=113[/tex]Associating like terms, that is, terms that have the same variable elevated to the same exponent:
[tex](8y+5y)+(2+7)=113[/tex]Adding like terms:
[tex]13y+9=113[/tex]Now we subtract 9 to both sides:
[tex]\begin{gathered} 13y+9-9=113-9 \\ 13y=104 \end{gathered}[/tex]Dividing both sides by 13
[tex]y=\frac{104}{13}=8[/tex]Now we replace the value of "y" in the expression for RS:
[tex]\begin{gathered} RS=8y+2 \\ RS=8(8)+2 \\ RS=64+2 \\ RS=66 \end{gathered}[/tex]Therefore, RS is 66.
