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Finding the Third Proportional to 65,043 and 97,014

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Solution

The third proportional to 65,043 and 97,014 is: 144,699.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,043 : 97,014 = 97,014 : x
  2. Step 2: Convert to fraction form
    65,043/97,014 = 97,014/x
  3. Step 3: Cross multiply
    65,043x = 97,014 × 97,014
  4. Step 4: Simplify right side
    65,043x = 9,411,716,196
  5. Step 5: Solve for x
    x = 9,411,716,196/65,043
  6. Step 6: Final answer
    x = 144,699.91

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.