A bag of sweets contains jellies, mints and toffees - OCR - GCSE Maths - Question 6 - 2021 - Paper 1
Question 6
A bag of sweets contains jellies, mints and toffees.
The ratio of jellies to mints is in n : 2.
The ratio of mints to toffees is 5 : 3n.
Work out the ratio of jell... show full transcript
Worked Solution & Example Answer:A bag of sweets contains jellies, mints and toffees - OCR - GCSE Maths - Question 6 - 2021 - Paper 1
Step 1
The ratio of jellies to mints is in n : 2
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Answer
Let the number of jellies be represented as n and the number of mints as 2. Thus, we can express this ratio as:
J:M=n:2.
Step 2
The ratio of mints to toffees is 5 : 3n
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Answer
Let the number of toffees be represented as T. The ratio of mints to toffees can be written as:
M:T=5:3n.
From the previous step, we know that the number of mints M=2. So we can express the ratio of mints to toffees as:
2:T=5:3n.
Step 3
Expressing T in terms of n
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Answer
From the ratio, we have:
rac{2}{T} = rac{5}{3n}.
Cross-multiplying gives:
2∗3n=5∗T
which simplifies to:
T = rac{6n}{5}.
Step 4
Finding the ratio of jellies to toffees
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Answer
Now that we have both the number of jellies and toffees, we can find the ratio:
Jellies to Toffees can be expressed as:
J : T = n : rac{6n}{5}.
This simplifies to:
J : T = n : rac{6n}{5} = 1 : rac{6}{5} = 5 : 6.
Thus, the ratio of jellies to toffees in simplest form is:
5:6.
