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Finding the Third Proportional to 1,023 and 1,531

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Solution

The third proportional to 1,023 and 1,531 is: 2,291.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023 : 1,531 = 1,531 : x
  2. Step 2: Convert to fraction form
    1,023/1,531 = 1,531/x
  3. Step 3: Cross multiply
    1,023x = 1,531 × 1,531
  4. Step 4: Simplify right side
    1,023x = 2,343,961
  5. Step 5: Solve for x
    x = 2,343,961/1,023
  6. Step 6: Final answer
    x = 2,291.26

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.