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Finding the Third Proportional to 5,700 and 8,498

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Solution

The third proportional to 5,700 and 8,498 is: 12,669.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,700 : 8,498 = 8,498 : x
  2. Step 2: Convert to fraction form
    5,700/8,498 = 8,498/x
  3. Step 3: Cross multiply
    5,700x = 8,498 × 8,498
  4. Step 4: Simplify right side
    5,700x = 72,216,004
  5. Step 5: Solve for x
    x = 72,216,004/5,700
  6. Step 6: Final answer
    x = 12,669.47

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.