Final answer:
The equation to solve the problem is 15x + 2(x - 6) = 260. Solving this equation, the number of bottles in a full case (x) is found to be 16. Consequently, there are 10 bottles in each partial case.
Step-by-step explanation:
The question asks about determining the number of soda bottles in full and partial cases when given the total number of bottles and the count of full and partial cases. We have 15 full cases of soda bottles and 2 cases that are missing 6 bottles each, and the total number of soda bottles is 260. To find the number of bottles in a full case, we'll let x represent the number of bottles in a full case.
Thus, the equation to represent this scenario is:
15x + 2(x - 6) = 260
Expanding and solving for x:
- 15x + 2x - 12 = 260
- 17x - 12 = 260
- 17x = 272
- x = 16
Therefore, there are 16 bottles in a full case. For the partial cases, since each is missing 6 bottles:
16 - 6 = 10 bottles in each of the partial cases.