Taylor has a full bottle of medicine. The bottle holds 20 doses of medicine. Each day Taylor takes one dose of medicine out of the bottle. After 8 days, there are 180 millilitres of medicine left in the bottle. Work out how many millilitres of medicine the bottle holds when full.

GCSE OCR Maths Proportion: Taylor has a full bottle of medi

Taylor has a full bottle of medicine - OCR - GCSE Maths - Question 7 - 2023 - Paper 5

Question 7

Taylor has a full bottle of medicine. The bottle holds 20 doses of medicine. Each day Taylor takes one dose of medicine out of the bottle. After 8 days, there are 18... show full transcript

Worked Solution & Example Answer:Taylor has a full bottle of medicine - OCR - GCSE Maths - Question 7 - 2023 - Paper 5

Step 1

Work out how much medicine was taken in 8 days

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Answer

Taylor takes 1 dose per day over 8 days, which means she takes a total of 8 doses. Since 20 doses are held in total, the amount of medicine taken is:

ext{Total doses} = ext{Initial doses} - ext{Medicine left} = 20 - rac{180}{x}

where x is the volume of each dose.

Step 2

Calculate the volume of each dose

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Answer

The volume of medicine left after 8 days is given as 180 ml, thus the initial full volume can be calculated as follows:

ext{Initial volume} = ext{Volume left} + ext{Volume taken} = 180 + (8 imes x)

Step 3

Set up the equation

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Answer

Substituting initial volume back, we can set up the equation:

20x = 180 + 8x

Step 4

Solve for x

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Answer

Rearranging gives:

20x - 8x = 180 \\n12x = 180 \\x = rac{180}{12} = 15 ext{ ml}

Step 5

Calculate the full volume of the bottle

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Answer

Now substituting x back, we find the total volume of the bottle:

ext{Total volume} = 20 imes 15 = 300 ext{ ml}

Taylor has a full bottle of medicine - OCR - GCSE Maths - Question 7 - 2023 - Paper 5

Worked Solution & Example Answer:Taylor has a full bottle of medicine - OCR - GCSE Maths - Question 7 - 2023 - Paper 5

Work out how much medicine was taken in 8 days

Calculate the volume of each dose

Set up the equation

Solve for x

Calculate the full volume of the bottle

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