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Finding the Third Proportional to 463,464 and 657,196

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Solution

The third proportional to 463,464 and 657,196 is: 931,909.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    463,464 : 657,196 = 657,196 : x
  2. Step 2: Convert to fraction form
    463,464/657,196 = 657,196/x
  3. Step 3: Cross multiply
    463,464x = 657,196 × 657,196
  4. Step 4: Simplify right side
    463,464x = 431,906,582,416
  5. Step 5: Solve for x
    x = 431,906,582,416/463,464
  6. Step 6: Final answer
    x = 931,909.67

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.