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Finding the Third Proportional to 678.38 and 1,421.93

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Solution

The third proportional to 678.38 and 1,421.93 is: 2,980.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    678.38 : 1,421.93 = 1,421.93 : x
  2. Step 2: Convert to fraction form
    678.38/1,421.93 = 1,421.93/x
  3. Step 3: Cross multiply
    678.38x = 1,421.93 × 1,421.93
  4. Step 4: Simplify right side
    678.38x = 2,021,884.04
  5. Step 5: Solve for x
    x = 2,021,884.04/678.38
  6. Step 6: Final answer
    x = 2,980.48

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.