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Finding the Third Proportional to 712 and 1,086

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Solution

The third proportional to 712 and 1,086 is: 1,656.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    712 : 1,086 = 1,086 : x
  2. Step 2: Convert to fraction form
    712/1,086 = 1,086/x
  3. Step 3: Cross multiply
    712x = 1,086 × 1,086
  4. Step 4: Simplify right side
    712x = 1,179,396
  5. Step 5: Solve for x
    x = 1,179,396/712
  6. Step 6: Final answer
    x = 1,656.46

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.