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Finding the Third Proportional to 462,070 and 578,407

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Solution

The third proportional to 462,070 and 578,407 is: 724,034.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    462,070 : 578,407 = 578,407 : x
  2. Step 2: Convert to fraction form
    462,070/578,407 = 578,407/x
  3. Step 3: Cross multiply
    462,070x = 578,407 × 578,407
  4. Step 4: Simplify right side
    462,070x = 334,554,657,649
  5. Step 5: Solve for x
    x = 334,554,657,649/462,070
  6. Step 6: Final answer
    x = 724,034.58

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Why These Related Problems?

These problems maintain the same ratio (1.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.