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Finding the Third Proportional to 653 and 1,028

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Solution

The third proportional to 653 and 1,028 is: 1,618.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    653 : 1,028 = 1,028 : x
  2. Step 2: Convert to fraction form
    653/1,028 = 1,028/x
  3. Step 3: Cross multiply
    653x = 1,028 × 1,028
  4. Step 4: Simplify right side
    653x = 1,056,784
  5. Step 5: Solve for x
    x = 1,056,784/653
  6. Step 6: Final answer
    x = 1,618.35

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.