Final answer:
To find the value of y, we add the equations for RS and ST, and set the sum equal to RT. Then we solve the resulting equation 11y + 8 = 74 to get y = 6, which is Option A.
Step-by-step explanation:
The student is tasked with finding the value of y when given the lengths of segments RS and ST, and the total length of RT. To solve for y, we use the fact that the sum of the lengths of segments RS and ST is equal to the length of segment RT. Specifically, RS + ST = RT.
For RS = 9y + 5 and ST = 2y + 3, adding these two equations gives us 9y + 5 + 2y + 3 = RT. We know that RT is 74, so substituting gives us 11y + 8 = 74. Solving for y requires subtracting 8 from both sides, which gives us 11y = 66, and then dividing both sides by 11 to isolate y, giving us y = 6.
Therefore, the correct value of y is 6, which corresponds to Option A.