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Finding the Third Proportional to 513.50 and 784.75

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Solution

The third proportional to 513.50 and 784.75 is: 1,199.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    513.50 : 784.75 = 784.75 : x
  2. Step 2: Convert to fraction form
    513.50/784.75 = 784.75/x
  3. Step 3: Cross multiply
    513.50x = 784.75 × 784.75
  4. Step 4: Simplify right side
    513.50x = 615,832.56
  5. Step 5: Solve for x
    x = 615,832.56/513.50
  6. Step 6: Final answer
    x = 1,199.28

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.