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Finding the Third Proportional to 405 and 560

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Solution

The third proportional to 405 and 560 is: 774.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    405 : 560 = 560 : x
  2. Step 2: Convert to fraction form
    405/560 = 560/x
  3. Step 3: Cross multiply
    405x = 560 × 560
  4. Step 4: Simplify right side
    405x = 313,600
  5. Step 5: Solve for x
    x = 313,600/405
  6. Step 6: Final answer
    x = 774.32

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.