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Finding the Third Proportional to 27,091 and 32,013

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Solution

The third proportional to 27,091 and 32,013 is: 37,829.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,091 : 32,013 = 32,013 : x
  2. Step 2: Convert to fraction form
    27,091/32,013 = 32,013/x
  3. Step 3: Cross multiply
    27,091x = 32,013 × 32,013
  4. Step 4: Simplify right side
    27,091x = 1,024,832,169
  5. Step 5: Solve for x
    x = 1,024,832,169/27,091
  6. Step 6: Final answer
    x = 37,829.25

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.