William W. answered • 10/03/19
Tutor
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Experienced Tutor and Retired Engineer
One theorem you should have studied is the Segment Addition Postulate which says: For A, B, & C on a segment, if B is between A & C, then the length of segment AB + the length of segment BC = the length of segment AC.
So, in your case, the length of segment RS + the length of segment ST = the length of segment RT and since RS = "9y + 3" and ST = "5y + 9" and RT = "124" then:
(9y + 3) + (5y + 9) = 124
combining like terms: 14y + 12 = 124 or 14y = 112 then dividing both sides by 14, y = 8
