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Finding the Third Proportional to 782.16 and 1,647.84

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Solution

The third proportional to 782.16 and 1,647.84 is: 3,471.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    782.16 : 1,647.84 = 1,647.84 : x
  2. Step 2: Convert to fraction form
    782.16/1,647.84 = 1,647.84/x
  3. Step 3: Cross multiply
    782.16x = 1,647.84 × 1,647.84
  4. Step 4: Simplify right side
    782.16x = 2,715,389.02
  5. Step 5: Solve for x
    x = 2,715,389.02/782.16
  6. Step 6: Final answer
    x = 3,471.67

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.