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Finding the Third Proportional to 6,458 and 7,046

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Solution

The third proportional to 6,458 and 7,046 is: 7,687.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,458 : 7,046 = 7,046 : x
  2. Step 2: Convert to fraction form
    6,458/7,046 = 7,046/x
  3. Step 3: Cross multiply
    6,458x = 7,046 × 7,046
  4. Step 4: Simplify right side
    6,458x = 49,646,116
  5. Step 5: Solve for x
    x = 49,646,116/6,458
  6. Step 6: Final answer
    x = 7,687.54

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.