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Finding the Third Proportional to 32,768 and 70,209

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Solution

The third proportional to 32,768 and 70,209 is: 150,430.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,768 : 70,209 = 70,209 : x
  2. Step 2: Convert to fraction form
    32,768/70,209 = 70,209/x
  3. Step 3: Cross multiply
    32,768x = 70,209 × 70,209
  4. Step 4: Simplify right side
    32,768x = 4,929,303,681
  5. Step 5: Solve for x
    x = 4,929,303,681/32,768
  6. Step 6: Final answer
    x = 150,430.41

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.