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Finding the Third Proportional to 380,362,116,523 and 829,068,047,522

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Solution

The third proportional to 380,362,116,523 and 829,068,047,522 is: 1,807,103,803,357.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    380,362,116,523 : 829,068,047,522 = 829,068,047,522 : x
  2. Step 2: Convert to fraction form
    380,362,116,523/829,068,047,522 = 829,068,047,522/x
  3. Step 3: Cross multiply
    380,362,116,523x = 829,068,047,522 × 829,068,047,522
  4. Step 4: Simplify right side
    380,362,116,523x = 687,353,827,421,941,252,751,360
  5. Step 5: Solve for x
    x = 687,353,827,421,941,252,751,360/380,362,116,523
  6. Step 6: Final answer
    x = 1,807,103,803,357.81

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.