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Finding the Third Proportional to 233,016 and 509,643

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Solution

The third proportional to 233,016 and 509,643 is: 1,114,670.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,016 : 509,643 = 509,643 : x
  2. Step 2: Convert to fraction form
    233,016/509,643 = 509,643/x
  3. Step 3: Cross multiply
    233,016x = 509,643 × 509,643
  4. Step 4: Simplify right side
    233,016x = 259,735,987,449
  5. Step 5: Solve for x
    x = 259,735,987,449/233,016
  6. Step 6: Final answer
    x = 1,114,670.18

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.