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Finding the Third Proportional to 1,285.25 and 1,420.25

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Solution

The third proportional to 1,285.25 and 1,420.25 is: 1,569.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,285.25 : 1,420.25 = 1,420.25 : x
  2. Step 2: Convert to fraction form
    1,285.25/1,420.25 = 1,420.25/x
  3. Step 3: Cross multiply
    1,285.25x = 1,420.25 × 1,420.25
  4. Step 4: Simplify right side
    1,285.25x = 2,017,110.06
  5. Step 5: Solve for x
    x = 2,017,110.06/1,285.25
  6. Step 6: Final answer
    x = 1,569.43

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.