MHB Using linear systems to solve problems (1)

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To determine when the cost of renting a car from Rent-a-Heap and Kurt's Rent-a-Car is the same, a linear equation can be set up based on their pricing structures. Rent-a-Heap charges $50 per day plus $0.12 per kilometer, while Kurt's Rent-a-Car charges $40 per day plus $0.20 per kilometer. The equations can be expressed as C = 50 + 0.12D for Rent-a-Heap and C = 40 + 0.20D for Kurt's. Setting these equations equal allows for solving the distance D at which both rental costs are identical. This approach utilizes linear systems to find the solution effectively.
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Sook-Lee wants to rent a car for a day so she can visit her sister at university. She has called two car rental agencies. Rent-a-Heap charges \$50 per day, plus \$0.12/km. Kurt's Rent-a-Car charges \$40 per day, plus \$0.20/km. At what distance will the cost of renting of a car be the same from companies?
 
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We are warned that it is a linear system. There should be a lot of y - mx + b going on. Maybe Ax + By = C.

Rules #1 - Name Stuff!

D = Daily Charge
M = Mileage Charge

Now what?
 
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* y = mx + b
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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