Charlie and Jasmine share cartons of apple juice. Charlie drinks $\frac{1}{3}$ of a carton every day. Jasmine drinks $\frac{2}{5}$ of a carton every day. Any apple juice left in a carton at the end of the day is used the following day. The cost of a carton is 70p. Charlie and Jasmine buy just enough cartons to last them for 10 days. How much do they spend in total for these cartons? Give your answer in £. Show your working.

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Charlie and Jasmine share cartons of apple juice - OCR - GCSE Maths - Question 5 - 2020 - Paper 1

Question 5

Charlie and Jasmine share cartons of apple juice. Charlie drinks $\frac{1}{3}$ of a carton every day. Jasmine drinks $\frac{2}{5}$ of a carton every day. Any appl... show full transcript

Worked Solution & Example Answer:Charlie and Jasmine share cartons of apple juice - OCR - GCSE Maths - Question 5 - 2020 - Paper 1

Step 1

Calculate the total daily consumption of apple juice

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Answer

Charlie's daily consumption: $\frac{1}{3}$ carton. Jasmine's daily consumption: $\frac{2}{5}$ carton.

To find the total daily consumption: $ext{Total Daily Consumption} = \frac{1}{3} + \frac{2}{5}$ To add these fractions, we need a common denominator, which is 15: $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$ So, $\text{Total Daily Consumption} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \text{ carton per day.}$

Step 2

Calculate the total consumption over 10 days

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Answer

Total consumption for 10 days: $10 \times \frac{11}{15} = \frac{110}{15} = 7.33 \text{ cartons.}$ Since they cannot buy a fraction of a carton, they will need to buy 8 cartons.

Step 3

Calculate the total cost of the cartons

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Answer

Cost of one carton is 70p. Total cost for 8 cartons: $8 \times 70p = 560p = £5.60$

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