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Finding the Third Proportional to 784.75 and 1,398.50

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Solution

The third proportional to 784.75 and 1,398.50 is: 2,492.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    784.75 : 1,398.50 = 1,398.50 : x
  2. Step 2: Convert to fraction form
    784.75/1,398.50 = 1,398.50/x
  3. Step 3: Cross multiply
    784.75x = 1,398.50 × 1,398.50
  4. Step 4: Simplify right side
    784.75x = 1,955,802.25
  5. Step 5: Solve for x
    x = 1,955,802.25/784.75
  6. Step 6: Final answer
    x = 2,492.26

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Why These Related Problems?

These problems maintain the same ratio (1.78) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.