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Finding the Third Proportional to 314 and 419.50

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Solution

The third proportional to 314 and 419.50 is: 560.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    314 : 419.50 = 419.50 : x
  2. Step 2: Convert to fraction form
    314/419.50 = 419.50/x
  3. Step 3: Cross multiply
    314x = 419.50 × 419.50
  4. Step 4: Simplify right side
    314x = 175,980.25
  5. Step 5: Solve for x
    x = 175,980.25/314
  6. Step 6: Final answer
    x = 560.45

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.