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Finding the Third Proportional to 563.50 and 1,257

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Solution

The third proportional to 563.50 and 1,257 is: 2,803.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    563.50 : 1,257 = 1,257 : x
  2. Step 2: Convert to fraction form
    563.50/1,257 = 1,257/x
  3. Step 3: Cross multiply
    563.50x = 1,257 × 1,257
  4. Step 4: Simplify right side
    563.50x = 1,580,049
  5. Step 5: Solve for x
    x = 1,580,049/563.50
  6. Step 6: Final answer
    x = 2,803.99

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.