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Finding the Third Proportional to 678.75 and 1,656.38

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Solution

The third proportional to 678.75 and 1,656.38 is: 4,042.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    678.75 : 1,656.38 = 1,656.38 : x
  2. Step 2: Convert to fraction form
    678.75/1,656.38 = 1,656.38/x
  3. Step 3: Cross multiply
    678.75x = 1,656.38 × 1,656.38
  4. Step 4: Simplify right side
    678.75x = 2,743,578.14
  5. Step 5: Solve for x
    x = 2,743,578.14/678.75
  6. Step 6: Final answer
    x = 4,042.10

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Why These Related Problems?

These problems maintain the same ratio (2.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.