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Finding the Third Proportional to 1,022 and 1,254

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Solution

The third proportional to 1,022 and 1,254 is: 1,538.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,022 : 1,254 = 1,254 : x
  2. Step 2: Convert to fraction form
    1,022/1,254 = 1,254/x
  3. Step 3: Cross multiply
    1,022x = 1,254 × 1,254
  4. Step 4: Simplify right side
    1,022x = 1,572,516
  5. Step 5: Solve for x
    x = 1,572,516/1,022
  6. Step 6: Final answer
    x = 1,538.67

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.