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Finding the Third Proportional to 294 and 410

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Solution

The third proportional to 294 and 410 is: 571.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    294 : 410 = 410 : x
  2. Step 2: Convert to fraction form
    294/410 = 410/x
  3. Step 3: Cross multiply
    294x = 410 × 410
  4. Step 4: Simplify right side
    294x = 168,100
  5. Step 5: Solve for x
    x = 168,100/294
  6. Step 6: Final answer
    x = 571.77

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These problems maintain the same ratio (1.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.