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Finding the Third Proportional to 233,024 and 509,658

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Solution

The third proportional to 233,024 and 509,658 is: 1,114,697.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,024 : 509,658 = 509,658 : x
  2. Step 2: Convert to fraction form
    233,024/509,658 = 509,658/x
  3. Step 3: Cross multiply
    233,024x = 509,658 × 509,658
  4. Step 4: Simplify right side
    233,024x = 259,751,276,964
  5. Step 5: Solve for x
    x = 259,751,276,964/233,024
  6. Step 6: Final answer
    x = 1,114,697.53

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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.