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5 and 9 with correct working - OCR - GCSE Maths - Question 12 - 2023 - Paper 5

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5 and 9 with correct working

Worked Solution & Example Answer:5 and 9 with correct working - OCR - GCSE Maths - Question 12 - 2023 - Paper 5

Step 1

Determine p and q using 2p + q = 112

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Answer

Starting from the equation, we can write:

2p+q=1122p + q = 112

If we denote this as (1), we will proceed to express q in terms of p.

Step 2

Use the equation to find specific values for p and q

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Answer

We can express q as:

q=112−2pq = 112 - 2p

Next, we substitute possible values for p to solve for q.

Step 3

Summarize the findings for p and q

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Answer

After testing various integer values for p such as 36 and 40, we find:

  • If p = 36, then q = 112 - 2(36) = 40
  • If p = 40, then q = 112 - 2(40) = 32

This yields valid pairs (p, q) = (36, 40) and (40, 32).

Step 4

Calculate the angles using p and q

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Answer

Using the relationships of angles:

  • If p equals 36, then one angle can be calculated as:
rac{p}{ ext{total degrees}} = rac{36}{360} ext{ implies angle } = rac{36}{360} imes 180 = 18 ext{ degrees}

Alternatively, if p equals 40, then:

ext{angle} = rac{40}{360} imes 180 = 20 ext{ degrees}

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