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Finding the Third Proportional to 432,584 and 578,646

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Solution

The third proportional to 432,584 and 578,646 is: 774,025.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    432,584 : 578,646 = 578,646 : x
  2. Step 2: Convert to fraction form
    432,584/578,646 = 578,646/x
  3. Step 3: Cross multiply
    432,584x = 578,646 × 578,646
  4. Step 4: Simplify right side
    432,584x = 334,831,193,316
  5. Step 5: Solve for x
    x = 334,831,193,316/432,584
  6. Step 6: Final answer
    x = 774,025.84

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.