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Finding the Third Proportional to 411,210 and 645,213

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Solution

The third proportional to 411,210 and 645,213 is: 1,012,377.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    411,210 : 645,213 = 645,213 : x
  2. Step 2: Convert to fraction form
    411,210/645,213 = 645,213/x
  3. Step 3: Cross multiply
    411,210x = 645,213 × 645,213
  4. Step 4: Simplify right side
    411,210x = 416,299,815,369
  5. Step 5: Solve for x
    x = 416,299,815,369/411,210
  6. Step 6: Final answer
    x = 1,012,377.65

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.