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Finding the Third Proportional to 4,178 and 6,506

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Solution

The third proportional to 4,178 and 6,506 is: 10,131.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,178 : 6,506 = 6,506 : x
  2. Step 2: Convert to fraction form
    4,178/6,506 = 6,506/x
  3. Step 3: Cross multiply
    4,178x = 6,506 × 6,506
  4. Step 4: Simplify right side
    4,178x = 42,328,036
  5. Step 5: Solve for x
    x = 42,328,036/4,178
  6. Step 6: Final answer
    x = 10,131.17

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.