Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box. Carlo puts a total of 3000 tins into the boxes so that number of tins in small boxes : number of tins in large boxes = 2 : 3 Carlo says that less than 30% of the boxes filled with tins are large boxes. Is Carlo correct? You must show all your working.

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Carlo puts tins into small boxes and into large boxes - Edexcel - GCSE Maths - Question 4 - 2020 - Paper 2

Question 4

Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box. Carlo puts a total of 3000 tins int... show full transcript

Worked Solution & Example Answer:Carlo puts tins into small boxes and into large boxes - Edexcel - GCSE Maths - Question 4 - 2020 - Paper 2

Step 1

Calculate the number of tins in small and large boxes

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Answer

Let the number of tins in small boxes be represented by 2x and in large boxes by 3x, according to the ratio given. Thus, we can form the equation:

2x + 3x = 3000

This simplifies to:

5x = 3000

From which we can solve for x:

x = \frac{3000}{5} = 600

So, the number of tins in small boxes is:

2x = 1200

And in large boxes is:

3x = 1800

Step 2

Determine the number of boxes

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Answer

Next, we calculate the number of boxes. The number of small boxes is:

\text{Number of small boxes} = \frac{\text{Total tins in small boxes}}{\text{Tins per small box}} = \frac{1200}{6} = 200

And the number of large boxes is:

\text{Number of large boxes} = \frac{\text{Total tins in large boxes}}{\text{Tins per large box}} = \frac{1800}{20} = 90

Step 3

Calculate total boxes and the percentage of large boxes

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Answer

The total number of boxes is:

\text{Total boxes} = \text{Number of small boxes} + \text{Number of large boxes} = 200 + 90 = 290

Now, to find the percentage of boxes that are large boxes:

\text{Percentage of large boxes} = \left( \frac{\text{Number of large boxes}}{\text{Total boxes}} \right) \times 100 = \left( \frac{90}{290} \right) \times 100 \approx 31.03\%

Since this is greater than 30%, Carlo's statement is incorrect.

Carlo puts tins into small boxes and into large boxes - Edexcel - GCSE Maths - Question 4 - 2020 - Paper 2

Worked Solution & Example Answer:Carlo puts tins into small boxes and into large boxes - Edexcel - GCSE Maths - Question 4 - 2020 - Paper 2

Calculate the number of tins in small and large boxes

Determine the number of boxes

Calculate total boxes and the percentage of large boxes

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