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Finding the Third Proportional to 2,065 and 3,097.50

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Solution

The third proportional to 2,065 and 3,097.50 is: 4,646.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,065 : 3,097.50 = 3,097.50 : x
  2. Step 2: Convert to fraction form
    2,065/3,097.50 = 3,097.50/x
  3. Step 3: Cross multiply
    2,065x = 3,097.50 × 3,097.50
  4. Step 4: Simplify right side
    2,065x = 9,594,506.25
  5. Step 5: Solve for x
    x = 9,594,506.25/2,065
  6. Step 6: Final answer
    x = 4,646.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.