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Finding the Third Proportional to 6,509 and 7,130

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Solution

The third proportional to 6,509 and 7,130 is: 7,810.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 7,130 = 7,130 : x
  2. Step 2: Convert to fraction form
    6,509/7,130 = 7,130/x
  3. Step 3: Cross multiply
    6,509x = 7,130 × 7,130
  4. Step 4: Simplify right side
    6,509x = 50,836,900
  5. Step 5: Solve for x
    x = 50,836,900/6,509
  6. Step 6: Final answer
    x = 7,810.25

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.