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let the number of bottles in the first group be B

Then

  • the 2nd group has 1st + 20 = B + 20 bottles;
  • the 3rd group has 2nd × 2 = 2 × (B + 20) = 2B + 40 bottles;
  • the 4th group has 3rd + 10 = 2B + 40 + 10 = 2B + 50 bottles.

The total number of bottles is the sum of the groups which is:

bottles = B + B + 20 + 2B + 40 + 2B + 50 = 6B + 110

But there are 1700 bottles, we can solve for B:

6B + 110 = 1700

→ 6B = 1590

→ B = 265

→ the groups contain:

  1. B = 265 bottles
  2. B + 20 = 265 + 20 = 285 bottles
  3. 2B + 40 = 530 + 40 = 570 bottles
  4. 2B + 50 = 530 + 50 = 580 bottles
Checking: 265 + 285 + 570 + 580 = 1700

The groups contain 265, 285, 570 and 580 bottles respectively.

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