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Finding the Third Proportional to 865 and 1,297.50

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Solution

The third proportional to 865 and 1,297.50 is: 1,946.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    865 : 1,297.50 = 1,297.50 : x
  2. Step 2: Convert to fraction form
    865/1,297.50 = 1,297.50/x
  3. Step 3: Cross multiply
    865x = 1,297.50 × 1,297.50
  4. Step 4: Simplify right side
    865x = 1,683,506.25
  5. Step 5: Solve for x
    x = 1,683,506.25/865
  6. Step 6: Final answer
    x = 1,946.25

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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.