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5 (a) Write 3 : 57 as a ratio in its simplest form - OCR - GCSE Maths - Question 5 - 2018 - Paper 1

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5 (a) Write 3 : 57 as a ratio in its simplest form. (b) Bob and Chris share some money in the ratio 2 : 3. Bob receives £8. Work out how much Chris receives.

Worked Solution & Example Answer:5 (a) Write 3 : 57 as a ratio in its simplest form - OCR - GCSE Maths - Question 5 - 2018 - Paper 1

Step 1

Write 3 : 57 as a ratio in its simplest form.

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Answer

To write the ratio 3 : 57 in its simplest form, we need to find the greatest common divisor (GCD) of 3 and 57. The GCD of 3 and 57 is 3.

To simplify, we divide both sides of the ratio by their GCD:

33:573=1:19\frac{3}{3} : \frac{57}{3} = 1 : 19

Thus, the simplest form of the ratio 3 : 57 is 1 : 19.

Step 2

Work out how much Chris receives.

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Answer

Bob and Chris share the money in the ratio 2 : 3. The total parts of the ratio are:

2+3=52 + 3 = 5

Given that Bob receives £8, we can calculate the value of one part:

Value of one part=82=£4\text{Value of one part} = \frac{8}{2} = £4

Now, to find out how much Chris receives, we multiply the value of one part by Chris's ratio part (3):

Chris’s amount=4×3=£12\text{Chris's amount} = 4 \times 3 = £12

Thus, Chris receives £12.

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