Answer: (3b+9) + (2b-2) = 67
That equation solves to b = 12. Meaning there are 12 water bottles in a full box.
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Step-by-step explanation
b = number of water bottles in each box
3b = number of water bottles in 3 boxes combined
3b+9 = add on the original 9 water bottles
2b = number of water bottles in 2 boxes combined
2b-2 = subtract off 2 water bottles because we take 1 water bottle from each previous box.
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Devin started with 9 water bottles. He adds on 3b water bottles to get 3b+9 so far. Then adds on another (2b-2) water bottles when adding 2 more boxes where each box has one missing water bottle. We can think of it like 2b-1 + 2b-1 = 2b-2
So we add those subtotals and set them equal to the grand total 67.
(3b+9) + (2b-2) = 67 which is one equation we could form.
Let's solve for variable b.
(3b+9) + (2b-2) = 67
(3b+2b) + (9-2) = 67
5b + 7 = 67
5b = 67-7
5b = 60
b = 60/5
b = 12
Each full box holds 12 water bottles (aka a dozen water bottles).
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Check:
1 box = 12 water bottles
3 boxes = 3*12 = 36 water bottles
2 boxes with 1 bottle missing per box = 2*12-1-1 = 22 water bottles
He started with 9 bottles, adds on 3 boxes (aka 36 water bottles) to get 9+36 = 45 water bottles so far. Then adds another 22 bottles to get 45+22 = 67 total. This matches up with what the instructions say. We have confirmed the answer is correct.