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Finding the Third Proportional to 456,518 and 686,157

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Solution

The third proportional to 456,518 and 686,157 is: 1,031,309.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    456,518 : 686,157 = 686,157 : x
  2. Step 2: Convert to fraction form
    456,518/686,157 = 686,157/x
  3. Step 3: Cross multiply
    456,518x = 686,157 × 686,157
  4. Step 4: Simplify right side
    456,518x = 470,811,428,649
  5. Step 5: Solve for x
    x = 470,811,428,649/456,518
  6. Step 6: Final answer
    x = 1,031,309.67

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.