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Finding the Third Proportional to 500 and 1,064

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Solution

The third proportional to 500 and 1,064 is: 2,264.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    500 : 1,064 = 1,064 : x
  2. Step 2: Convert to fraction form
    500/1,064 = 1,064/x
  3. Step 3: Cross multiply
    500x = 1,064 × 1,064
  4. Step 4: Simplify right side
    500x = 1,132,096
  5. Step 5: Solve for x
    x = 1,132,096/500
  6. Step 6: Final answer
    x = 2,264.19

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.