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Finding the Third Proportional to 7,784 and 11,117

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Solution

The third proportional to 7,784 and 11,117 is: 15,877.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,784 : 11,117 = 11,117 : x
  2. Step 2: Convert to fraction form
    7,784/11,117 = 11,117/x
  3. Step 3: Cross multiply
    7,784x = 11,117 × 11,117
  4. Step 4: Simplify right side
    7,784x = 123,587,689
  5. Step 5: Solve for x
    x = 123,587,689/7,784
  6. Step 6: Final answer
    x = 15,877.14

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.