Final answer:
To find the value of n, set up the equation SU = ST + TU using the provided expressions and solve for n. After simplifying the equation, the value of n is found to be 3.
Step-by-step explanation:
The problem stated is a classic example of a segment addition in algebra where a line segment is divided into parts. Here, the line segment is SU and is divided into two parts ST and TU by point T. The problem can be solved in the following steps:
- Understand that the whole is equal to the sum of its parts, so SU = ST + TU.
- Write the equation using the given expressions: (40n-40) = (20n-2) + (5n + 7).
- Simplify and solve for n by combining like terms and isolating n.
Step one requires knowing that point T is between S and U and therefore ST plus TU must equal SU. Substituting the given values gives us:
40n - 40 = (20n - 2) + (5n + 7)
Combining like terms leads to:
40n - 40 = 25n + 5
Subtracting 25n from both sides we get:
15n - 40 = 5
Adding 40 to both sides we find:
15n = 45
Dividing both sides by 15:
n = 3
The value of n is therefore 3.