Final answer:
After solving the equations by setting the sum of Ef and Gf equal to eg (28), we find that x=8, ef=11, and fg=17. However, this solution does not match the provided answer choices, suggesting an error in the question or choices.
Step-by-step explanation:
The question presents three equations representing lengths or distances (Ef, Gf, and eg) and asks to solve for x, ef, and fg. The eg (which likely represents the sum of ef and fg) is given as 28. The equations given are Ef = 3x - 13 and Gf = 4x - 15. To solve for x, we set Ef + fg to equal eg (because ef + fg = eg), and substitute Ef and Gf into that equation: (3x - 13) + (4x - 15) = 28.
Combining like terms results in 7x - 28 = 28. Adding 28 to both sides gives us 7x = 56, and dividing both sides by 7 results in x = 8. We can now substitute x back into the equations for Ef and Gf to find their values: Ef = 3(8) - 13 = 24 - 13 = 11, and Gf = 4(8) - 15 = 32 - 15 = 17.
The length of fg can be found by subtracting the length of Ef from eg: fg = eg - Ef = 28 - 11 = 17. Therefore, the correct values are x = 8, ef = 11, and fg = 17. However, this set of values is not listed among the provided answer choices, indicating there might be a typo either in the question or the choices.