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Finding the Third Proportional to 9,784 and 22,984

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Solution

The third proportional to 9,784 and 22,984 is: 53,992.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,784 : 22,984 = 22,984 : x
  2. Step 2: Convert to fraction form
    9,784/22,984 = 22,984/x
  3. Step 3: Cross multiply
    9,784x = 22,984 × 22,984
  4. Step 4: Simplify right side
    9,784x = 528,264,256
  5. Step 5: Solve for x
    x = 528,264,256/9,784
  6. Step 6: Final answer
    x = 53,992.67

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.