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Finding the Third Proportional to 772 and 1,777

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Solution

The third proportional to 772 and 1,777 is: 4,090.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    772 : 1,777 = 1,777 : x
  2. Step 2: Convert to fraction form
    772/1,777 = 1,777/x
  3. Step 3: Cross multiply
    772x = 1,777 × 1,777
  4. Step 4: Simplify right side
    772x = 3,157,729
  5. Step 5: Solve for x
    x = 3,157,729/772
  6. Step 6: Final answer
    x = 4,090.32

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.