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Finding the Third Proportional to 774.75 and 1,538.25

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Solution

The third proportional to 774.75 and 1,538.25 is: 3,054.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    774.75 : 1,538.25 = 1,538.25 : x
  2. Step 2: Convert to fraction form
    774.75/1,538.25 = 1,538.25/x
  3. Step 3: Cross multiply
    774.75x = 1,538.25 × 1,538.25
  4. Step 4: Simplify right side
    774.75x = 2,366,213.06
  5. Step 5: Solve for x
    x = 2,366,213.06/774.75
  6. Step 6: Final answer
    x = 3,054.16

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Why These Related Problems?

These problems maintain the same ratio (1.99) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.