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Finding the Third Proportional to 232.50 and 407.50

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Solution

The third proportional to 232.50 and 407.50 is: 714.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    232.50 : 407.50 = 407.50 : x
  2. Step 2: Convert to fraction form
    232.50/407.50 = 407.50/x
  3. Step 3: Cross multiply
    232.50x = 407.50 × 407.50
  4. Step 4: Simplify right side
    232.50x = 166,056.25
  5. Step 5: Solve for x
    x = 166,056.25/232.50
  6. Step 6: Final answer
    x = 714.22

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Why These Related Problems?

These problems maintain the same ratio (1.75) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.