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Finding the Third Proportional to 76,776 and 117,030

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Solution

The third proportional to 76,776 and 117,030 is: 178,389.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,776 : 117,030 = 117,030 : x
  2. Step 2: Convert to fraction form
    76,776/117,030 = 117,030/x
  3. Step 3: Cross multiply
    76,776x = 117,030 × 117,030
  4. Step 4: Simplify right side
    76,776x = 13,696,020,900
  5. Step 5: Solve for x
    x = 13,696,020,900/76,776
  6. Step 6: Final answer
    x = 178,389.35

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.