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Finding the Third Proportional to 2,160 and 2,358

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Solution

The third proportional to 2,160 and 2,358 is: 2,574.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,160 : 2,358 = 2,358 : x
  2. Step 2: Convert to fraction form
    2,160/2,358 = 2,358/x
  3. Step 3: Cross multiply
    2,160x = 2,358 × 2,358
  4. Step 4: Simplify right side
    2,160x = 5,560,164
  5. Step 5: Solve for x
    x = 5,560,164/2,160
  6. Step 6: Final answer
    x = 2,574.15

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.