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Finding the Third Proportional to 690 and 1,038

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Solution

The third proportional to 690 and 1,038 is: 1,561.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    690 : 1,038 = 1,038 : x
  2. Step 2: Convert to fraction form
    690/1,038 = 1,038/x
  3. Step 3: Cross multiply
    690x = 1,038 × 1,038
  4. Step 4: Simplify right side
    690x = 1,077,444
  5. Step 5: Solve for x
    x = 1,077,444/690
  6. Step 6: Final answer
    x = 1,561.51

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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.