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Finding the Third Proportional to 7,578 and 16,209

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Solution

The third proportional to 7,578 and 16,209 is: 34,670.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,578 : 16,209 = 16,209 : x
  2. Step 2: Convert to fraction form
    7,578/16,209 = 16,209/x
  3. Step 3: Cross multiply
    7,578x = 16,209 × 16,209
  4. Step 4: Simplify right side
    7,578x = 262,731,681
  5. Step 5: Solve for x
    x = 262,731,681/7,578
  6. Step 6: Final answer
    x = 34,670.32

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.