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Finding the Third Proportional to 261.75 and 412.88

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Solution

The third proportional to 261.75 and 412.88 is: 651.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    261.75 : 412.88 = 412.88 : x
  2. Step 2: Convert to fraction form
    261.75/412.88 = 412.88/x
  3. Step 3: Cross multiply
    261.75x = 412.88 × 412.88
  4. Step 4: Simplify right side
    261.75x = 170,465.77
  5. Step 5: Solve for x
    x = 170,465.77/261.75
  6. Step 6: Final answer
    x = 651.25

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.