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Finding the Third Proportional to 420.19 and 974.53

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Solution

The third proportional to 420.19 and 974.53 is: 2,260.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    420.19 : 974.53 = 974.53 : x
  2. Step 2: Convert to fraction form
    420.19/974.53 = 974.53/x
  3. Step 3: Cross multiply
    420.19x = 974.53 × 974.53
  4. Step 4: Simplify right side
    420.19x = 949,711.16
  5. Step 5: Solve for x
    x = 949,711.16/420.19
  6. Step 6: Final answer
    x = 2,260.21

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.