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Finding the Third Proportional to 6,509 and 14,224

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Solution

The third proportional to 6,509 and 14,224 is: 31,083.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 14,224 = 14,224 : x
  2. Step 2: Convert to fraction form
    6,509/14,224 = 14,224/x
  3. Step 3: Cross multiply
    6,509x = 14,224 × 14,224
  4. Step 4: Simplify right side
    6,509x = 202,322,176
  5. Step 5: Solve for x
    x = 202,322,176/6,509
  6. Step 6: Final answer
    x = 31,083.45

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.