Final answer:
To find BC, we set up the equation 4y + 11 + 10y + 5 = 16y - 22, solve for y, and then substitute back into the expression for BC, yielding a final value of 195 for BC's length.
Step-by-step explanation:
The question involves solving for the length of segment BC given that points A, B, and C are collinear with point B between A and C, and the lengths AB, BC, and AC are represented by the expressions 4y + 11, 10y + 5, and 16y - 22, respectively.
Step-by-Step Solution:
Since AB + BC = AC, we can write the equation 4y + 11 + 10y + 5 = 16y - 22.
Now we combine like terms, resulting in 14y + 16 = 16y - 22.
Next, we subtract 14y from both sides of the equation, this gives us 16 = 2y - 22.
Adding 22 to both sides yields 38 = 2y.
Finally, we divide both sides by 2 to find y, resulting in y = 19.
To find BC, we substitute y back into the expression for BC: 10y + 5, which gives us 10(19) + 5, hence BC = 195.