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Finding the Third Proportional to 6,440 and 7,106

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Solution

The third proportional to 6,440 and 7,106 is: 7,840.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,440 : 7,106 = 7,106 : x
  2. Step 2: Convert to fraction form
    6,440/7,106 = 7,106/x
  3. Step 3: Cross multiply
    6,440x = 7,106 × 7,106
  4. Step 4: Simplify right side
    6,440x = 50,495,236
  5. Step 5: Solve for x
    x = 50,495,236/6,440
  6. Step 6: Final answer
    x = 7,840.88

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.