Question

If EF = 3x - 13, FG = 4x - 11, and EG = 25, find the values of x, EF, and FG. The drawing is not to scale.

A) x = 2, EF = -7, FG = -3
B) x = 7, EF = 34, FG = 39
C) x = 2, EF = 8, FG = 17
D) x = 7, EF = 8, FG = 17

Answer 1

Upon solving the system of equations given by EF, FG, and EG, we find that x equals 7, EF equals 8, and FG equals 17.

Step-by-step explanation:

We’re given that EF = 3x - 13, FG = 4x - 11, and EG = 25. Since EF and FG are parts of line segment EG, we can set up the equation:

EF + FG = EG

(3x - 13) + (4x - 11) = 25

Adding the like terms we get:

7x - 24 = 25

Adding 24 to both sides gives us:

7x = 49

When we divide both sides by 7, we find:

x = 7

Substituting the value of x into the original equations gives us:

EF = 3x - 13 = 3(7) - 13 = 21 - 13 = 8

and

FG = 4x - 11 = 4(7) - 11 = 28 - 11 = 17

Hence, the correct values are x = 7, EF = 8, and FG = 17.