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Finding the Third Proportional to 414,088 and 586,056

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Solution

The third proportional to 414,088 and 586,056 is: 829,441.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    414,088 : 586,056 = 586,056 : x
  2. Step 2: Convert to fraction form
    414,088/586,056 = 586,056/x
  3. Step 3: Cross multiply
    414,088x = 586,056 × 586,056
  4. Step 4: Simplify right side
    414,088x = 343,461,635,136
  5. Step 5: Solve for x
    x = 343,461,635,136/414,088
  6. Step 6: Final answer
    x = 829,441.17

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.