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Finding the Third Proportional to 5,724 and 9,140

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Solution

The third proportional to 5,724 and 9,140 is: 14,594.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,724 : 9,140 = 9,140 : x
  2. Step 2: Convert to fraction form
    5,724/9,140 = 9,140/x
  3. Step 3: Cross multiply
    5,724x = 9,140 × 9,140
  4. Step 4: Simplify right side
    5,724x = 83,539,600
  5. Step 5: Solve for x
    x = 83,539,600/5,724
  6. Step 6: Final answer
    x = 14,594.62

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.