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Finding the Third Proportional to 5,214 and 9,085

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Solution

The third proportional to 5,214 and 9,085 is: 15,829.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,214 : 9,085 = 9,085 : x
  2. Step 2: Convert to fraction form
    5,214/9,085 = 9,085/x
  3. Step 3: Cross multiply
    5,214x = 9,085 × 9,085
  4. Step 4: Simplify right side
    5,214x = 82,537,225
  5. Step 5: Solve for x
    x = 82,537,225/5,214
  6. Step 6: Final answer
    x = 15,829.92

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Why These Related Problems?

These problems maintain the same ratio (1.74) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.