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Finding the Third Proportional to 402 and 712

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Solution

The third proportional to 402 and 712 is: 1,261.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    402 : 712 = 712 : x
  2. Step 2: Convert to fraction form
    402/712 = 712/x
  3. Step 3: Cross multiply
    402x = 712 × 712
  4. Step 4: Simplify right side
    402x = 506,944
  5. Step 5: Solve for x
    x = 506,944/402
  6. Step 6: Final answer
    x = 1,261.05

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.