p and q are two numbers such that $p > q$ - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 2
Question 17
p and q are two numbers such that $p > q$.
When you subtract 5 from p and subtract 5 from q the answers are in the ratio 5:1.
When you add 20 to p and add 20 to q t... show full transcript
Worked Solution & Example Answer:p and q are two numbers such that $p > q$ - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 2
Step 1
When you subtract 5 from p and subtract 5 from q the answers are in the ratio 5:1.
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Answer
We know that when subtracting 5 from both numbers, the relationship can be set as:
rac{p - 5}{q - 5} = rac{5}{1}
By cross-multiplying, we get:
p−5=5(q−5)
Expanding this leads to:
p−5=5q−25
Then rearranging gives us our first equation:
p−5q=−20ag1
Step 2
When you add 20 to p and add 20 to q the answers are in the ratio 5:2.
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Answer
For the second condition, we have:
rac{p + 20}{q + 20} = rac{5}{2}
Cross-multiplying results in:
2(p+20)=5(q+20)
Expanding yields:
2p+40=5q+100
And rearranging gives us another equation:
2p−5q=60ag2
Step 3
Solve the equations to find p and q.
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Answer
We can now solve the two equations:
p−5q=−20
2p−5q=60
From (1), we can express p in terms of q:
p=5q−20ag3
Substituting equation (3) into equation (2):
2(5q−20)−5q=60
This simplifies to:
10q−40−5q=60
Which leads to:
5q=100
Thus, we find:
q=20
Substituting q back into equation (3):
p=5(20)−20=100−20=80
Therefore, we have p=80 and q=20.
Step 4
Find the ratio p:q.
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Answer
Finally, the ratio of p to q is:
p:q=80:20
This simplifies to:
p:q=4:1.
Thus, the final answer is in its simplest form: 4:1.
