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Finding the Third Proportional to 509,772 and 712,998

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Solution

The third proportional to 509,772 and 712,998 is: 997,242.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    509,772 : 712,998 = 712,998 : x
  2. Step 2: Convert to fraction form
    509,772/712,998 = 712,998/x
  3. Step 3: Cross multiply
    509,772x = 712,998 × 712,998
  4. Step 4: Simplify right side
    509,772x = 508,366,148,004
  5. Step 5: Solve for x
    x = 508,366,148,004/509,772
  6. Step 6: Final answer
    x = 997,242.19

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.