Using proportions, it is found that they spent a total of £5.6 for these cartons of apple juice.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the daily fraction of a carton they drink is given by:
[tex]\frac{1}{3} + \frac{2}{5} = \frac{5 + 6}{15} = \frac{11}{15}[/tex]
Hence, applying the proportion, over 10 days, the amount of cartons they drink is given by:
[tex]10 \times \frac{11}{15} = \frac{110}{15} = 7.33[/tex]
Rounding up, they buy 8 cartons, each at £0.7. Hence the total amount spent is given by:
8 x £0.7 = £5.6.
More can be learned about proportions at https://brainly.com/question/24372153
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