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Finding the Third Proportional to 7,830 and 12,457

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Solution

The third proportional to 7,830 and 12,457 is: 19,818.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,830 : 12,457 = 12,457 : x
  2. Step 2: Convert to fraction form
    7,830/12,457 = 12,457/x
  3. Step 3: Cross multiply
    7,830x = 12,457 × 12,457
  4. Step 4: Simplify right side
    7,830x = 155,176,849
  5. Step 5: Solve for x
    x = 155,176,849/7,830
  6. Step 6: Final answer
    x = 19,818.24

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.