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Finding the Third Proportional to 786 and 1,166

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Solution

The third proportional to 786 and 1,166 is: 1,729.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    786 : 1,166 = 1,166 : x
  2. Step 2: Convert to fraction form
    786/1,166 = 1,166/x
  3. Step 3: Cross multiply
    786x = 1,166 × 1,166
  4. Step 4: Simplify right side
    786x = 1,359,556
  5. Step 5: Solve for x
    x = 1,359,556/786
  6. Step 6: Final answer
    x = 1,729.72

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.