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Finding the Third Proportional to 698 and 1,037

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Solution

The third proportional to 698 and 1,037 is: 1,540.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    698 : 1,037 = 1,037 : x
  2. Step 2: Convert to fraction form
    698/1,037 = 1,037/x
  3. Step 3: Cross multiply
    698x = 1,037 × 1,037
  4. Step 4: Simplify right side
    698x = 1,075,369
  5. Step 5: Solve for x
    x = 1,075,369/698
  6. Step 6: Final answer
    x = 1,540.64

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.