Answer:
[tex]y=8[/tex]
[tex]RS=77, ST=31[/tex]
Step-by-step explanation:
Note that the entire segment RT is the combined lengths of RS and ST. So:
[tex]RT=RS+ST[/tex]
We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:
[tex]108=(9y+5)+(3y+7)[/tex]
On the right, combine like terms:
[tex]108=(9y+3y)+(5+7)[/tex]
Add:
[tex]108=12y+12[/tex]
Subtract 12 from both sides. The right cancels:
[tex]96=12y[/tex]
Divide both sides by 12:
[tex]y=8[/tex]
So, the value of y is 8.
To find RS and ST, substitute 8 for y. So:
[tex]RS=9y+5[/tex]
Substitute 8 for y:
[tex]RS=9(8)+5[/tex]
Multiply:
[tex]RS=72+5[/tex]
Add:
[tex]RS=77[/tex]
Do the same for ST:
[tex]ST=3y+7[/tex]
Substitute 8 for y:
[tex]ST=3(8)+7[/tex]
Multiply:
[tex]ST=24+7[/tex]
Add:
[tex]ST=31[/tex]
