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Finding the Third Proportional to 311,902 and 470,071

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Solution

The third proportional to 311,902 and 470,071 is: 708,449.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,902 : 470,071 = 470,071 : x
  2. Step 2: Convert to fraction form
    311,902/470,071 = 470,071/x
  3. Step 3: Cross multiply
    311,902x = 470,071 × 470,071
  4. Step 4: Simplify right side
    311,902x = 220,966,745,041
  5. Step 5: Solve for x
    x = 220,966,745,041/311,902
  6. Step 6: Final answer
    x = 708,449.27

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.