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Finding the Third Proportional to 565 and 1,026.50

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Solution

The third proportional to 565 and 1,026.50 is: 1,864.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    565 : 1,026.50 = 1,026.50 : x
  2. Step 2: Convert to fraction form
    565/1,026.50 = 1,026.50/x
  3. Step 3: Cross multiply
    565x = 1,026.50 × 1,026.50
  4. Step 4: Simplify right side
    565x = 1,053,702.25
  5. Step 5: Solve for x
    x = 1,053,702.25/565
  6. Step 6: Final answer
    x = 1,864.96

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Why These Related Problems?

These problems maintain the same ratio (1.82) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.