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Finding the Third Proportional to 260 and 286.50

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Solution

The third proportional to 260 and 286.50 is: 315.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    260 : 286.50 = 286.50 : x
  2. Step 2: Convert to fraction form
    260/286.50 = 286.50/x
  3. Step 3: Cross multiply
    260x = 286.50 × 286.50
  4. Step 4: Simplify right side
    260x = 82,082.25
  5. Step 5: Solve for x
    x = 82,082.25/260
  6. Step 6: Final answer
    x = 315.70

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.