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Finding the Third Proportional to 709 and 1,178

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Solution

The third proportional to 709 and 1,178 is: 1,957.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    709 : 1,178 = 1,178 : x
  2. Step 2: Convert to fraction form
    709/1,178 = 1,178/x
  3. Step 3: Cross multiply
    709x = 1,178 × 1,178
  4. Step 4: Simplify right side
    709x = 1,387,684
  5. Step 5: Solve for x
    x = 1,387,684/709
  6. Step 6: Final answer
    x = 1,957.24

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.