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Finding the Third Proportional to 1,209 and 1,537

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Solution

The third proportional to 1,209 and 1,537 is: 1,953.99

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,209 : 1,537 = 1,537 : x
  2. Step 2: Convert to fraction form
    1,209/1,537 = 1,537/x
  3. Step 3: Cross multiply
    1,209x = 1,537 × 1,537
  4. Step 4: Simplify right side
    1,209x = 2,362,369
  5. Step 5: Solve for x
    x = 2,362,369/1,209
  6. Step 6: Final answer
    x = 1,953.99

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.