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Finding the Third Proportional to 32,042 and 71,077

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Solution

The third proportional to 32,042 and 71,077 is: 157,666.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,042 : 71,077 = 71,077 : x
  2. Step 2: Convert to fraction form
    32,042/71,077 = 71,077/x
  3. Step 3: Cross multiply
    32,042x = 71,077 × 71,077
  4. Step 4: Simplify right side
    32,042x = 5,051,939,929
  5. Step 5: Solve for x
    x = 5,051,939,929/32,042
  6. Step 6: Final answer
    x = 157,666.19

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.