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Finding the Third Proportional to 257.50 and 538.50

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Solution

The third proportional to 257.50 and 538.50 is: 1,126.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.50 : 538.50 = 538.50 : x
  2. Step 2: Convert to fraction form
    257.50/538.50 = 538.50/x
  3. Step 3: Cross multiply
    257.50x = 538.50 × 538.50
  4. Step 4: Simplify right side
    257.50x = 289,982.25
  5. Step 5: Solve for x
    x = 289,982.25/257.50
  6. Step 6: Final answer
    x = 1,126.14

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.