Math Problem Statement
Solution
The problem shown in the image presents a situation where different routes from "Home" to "School" involve different points of reference: the "Mall" and the "Theater." The distances between each point are expressed in terms of . The goal is to solve for using the given information that the total distance passing through the Mall equals the total distance passing through the Theater.
Part 7a: Setting up the equation
-
Route passing through the Mall:
- Distance from Home to Mall:
- Distance from Mall to School:
- Total distance:
-
Route passing through the Theater:
- Distance from Home to Theater:
- Distance from Theater to School:
- Total distance:
Since the problem states that these two routes are the same, you can set the total distances equal to each other:
Solving for :
Subtract from both sides: Subtract 1 from both sides:
Part 7b: Finding the total distance from Home to School
Now that we know , we can plug this value back into either route to find the total distance. Let's use the route through the Mall:
Therefore, the total distance from Home to School is 7 miles.
Would you like any more details or have any questions?
Related Questions:
- How would the equation change if the distance from Home to Mall was instead of ?
- What if the distance from Theater to School was instead of ?
- How do you solve systems of linear equations with more than two variables?
- How can you verify that both routes still give the same total distance for different values of ?
- How would the total distance change if was negative?
Tip:
Always double-check the distances before solving for by writing out each total route explicitly!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Total distance = Distance from Home to Mall + Distance from Mall to School
Total distance = Distance from Home to Theater + Distance from Theater to School
Theorems
Linear Equations Theorem
Suitable Grade Level
Grades 7-9
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