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Finding the Third Proportional to 654 and 711.75

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Solution

The third proportional to 654 and 711.75 is: 774.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    654 : 711.75 = 711.75 : x
  2. Step 2: Convert to fraction form
    654/711.75 = 711.75/x
  3. Step 3: Cross multiply
    654x = 711.75 × 711.75
  4. Step 4: Simplify right side
    654x = 506,588.06
  5. Step 5: Solve for x
    x = 506,588.06/654
  6. Step 6: Final answer
    x = 774.60

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.