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Finding the Third Proportional to 314,557 and 684,409

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Solution

The third proportional to 314,557 and 684,409 is: 1,489,128.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    314,557 : 684,409 = 684,409 : x
  2. Step 2: Convert to fraction form
    314,557/684,409 = 684,409/x
  3. Step 3: Cross multiply
    314,557x = 684,409 × 684,409
  4. Step 4: Simplify right side
    314,557x = 468,415,679,281
  5. Step 5: Solve for x
    x = 468,415,679,281/314,557
  6. Step 6: Final answer
    x = 1,489,128.14

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.