Math Problem Statement
Solution
Let's break down the problem step by step.
We are given:
The total segment is the sum of and , so we can set up the following equation:
Now, simplify the left side:
Combine like terms:
Add 27 to both sides:
Now, divide by 5:
Now that we know , substitute this value into the expressions for and :
Thus, the values are:
The correct answer is:
This corresponds to the first option: .
Would you like further details or clarification? Here are five related questions to expand this concept:
- How do you calculate the length of a segment when multiple subsegments are given algebraically?
- What happens if the sum of is less than the total ?
- How would the solution change if the equations for and involved different coefficients for ?
- How can you visualize this problem on a number line or with a geometric drawing?
- What strategies can be used to check if the solution to the system of equations is correct?
Tip: Always ensure that the total segment length matches the sum of the individual parts when solving segment problems in geometry!
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Linear Equations
Formulas
EF = 2x - 12
FG = 3x - 15
EG = EF + FG
Theorems
Addition of segments in geometry
Suitable Grade Level
Grade 8-10