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Finding the Third Proportional to 507 and 782.25

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Solution

The third proportional to 507 and 782.25 is: 1,206.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    507 : 782.25 = 782.25 : x
  2. Step 2: Convert to fraction form
    507/782.25 = 782.25/x
  3. Step 3: Cross multiply
    507x = 782.25 × 782.25
  4. Step 4: Simplify right side
    507x = 611,915.06
  5. Step 5: Solve for x
    x = 611,915.06/507
  6. Step 6: Final answer
    x = 1,206.93

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.