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Finding the Fourth Proportional to 977, 1,465.63 and 456.93

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Solution

The fourth proportional to 977, 1,465.63 and 456.93 is: 685.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,465.63 = 456.93 : x
  2. Step 2: Convert to fraction form
    977/1,465.63 = 456.93/x
  3. Step 3: Cross multiply
    977x = 1,465.63 × 456.93
  4. Step 4: Simplify right side
    977x = 669,690.32
  5. Step 5: Solve for x
    x = 669,690.32/977
  6. Step 6: Final answer
    x = 685.46

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.