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Finding the Third Proportional to 7,834 and 14,570

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Solution

The third proportional to 7,834 and 14,570 is: 27,097.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,834 : 14,570 = 14,570 : x
  2. Step 2: Convert to fraction form
    7,834/14,570 = 14,570/x
  3. Step 3: Cross multiply
    7,834x = 14,570 × 14,570
  4. Step 4: Simplify right side
    7,834x = 212,284,900
  5. Step 5: Solve for x
    x = 212,284,900/7,834
  6. Step 6: Final answer
    x = 27,097.89

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.