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Finding the Third Proportional to 1,077.75 and 1,409.06

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Solution

The third proportional to 1,077.75 and 1,409.06 is: 1,842.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,077.75 : 1,409.06 = 1,409.06 : x
  2. Step 2: Convert to fraction form
    1,077.75/1,409.06 = 1,409.06/x
  3. Step 3: Cross multiply
    1,077.75x = 1,409.06 × 1,409.06
  4. Step 4: Simplify right side
    1,077.75x = 1,985,457.13
  5. Step 5: Solve for x
    x = 1,985,457.13/1,077.75
  6. Step 6: Final answer
    x = 1,842.22

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.