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Finding the Third Proportional to 1,026 and 1,310

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Solution

The third proportional to 1,026 and 1,310 is: 1,672.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,026 : 1,310 = 1,310 : x
  2. Step 2: Convert to fraction form
    1,026/1,310 = 1,310/x
  3. Step 3: Cross multiply
    1,026x = 1,310 × 1,310
  4. Step 4: Simplify right side
    1,026x = 1,716,100
  5. Step 5: Solve for x
    x = 1,716,100/1,026
  6. Step 6: Final answer
    x = 1,672.61

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.