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Finding the Third Proportional to 712 and 1,646

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Solution

The third proportional to 712 and 1,646 is: 3,805.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    712 : 1,646 = 1,646 : x
  2. Step 2: Convert to fraction form
    712/1,646 = 1,646/x
  3. Step 3: Cross multiply
    712x = 1,646 × 1,646
  4. Step 4: Simplify right side
    712x = 2,709,316
  5. Step 5: Solve for x
    x = 2,709,316/712
  6. Step 6: Final answer
    x = 3,805.22

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.