Thomas In most tax systems this is not allowed. The above suggested way seems legal, as the costs are charged to the business and thus are deductible.
You should however note that some tax systems require you to report the costs of the private accounts as turnover, which means the extra costs of the pack (compared to the costs of a single business account) aren’t deductible from your profit.
Ask your bookkeeper or accountant what rules apply in your taxation system.