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Finding the Third Proportional to 3,584 and 7,842

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Solution

The third proportional to 3,584 and 7,842 is: 17,158.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,584 : 7,842 = 7,842 : x
  2. Step 2: Convert to fraction form
    3,584/7,842 = 7,842/x
  3. Step 3: Cross multiply
    3,584x = 7,842 × 7,842
  4. Step 4: Simplify right side
    3,584x = 61,496,964
  5. Step 5: Solve for x
    x = 61,496,964/3,584
  6. Step 6: Final answer
    x = 17,158.75

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.