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Finding the Third Proportional to 165 and 420.50

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Solution

The third proportional to 165 and 420.50 is: 1,071.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    165 : 420.50 = 420.50 : x
  2. Step 2: Convert to fraction form
    165/420.50 = 420.50/x
  3. Step 3: Cross multiply
    165x = 420.50 × 420.50
  4. Step 4: Simplify right side
    165x = 176,820.25
  5. Step 5: Solve for x
    x = 176,820.25/165
  6. Step 6: Final answer
    x = 1,071.64

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Why These Related Problems?

These problems maintain the same ratio (2.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.