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.

GCSE Edexcel Maths Completing the Square: Carlo puts tins into small boxes

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

total tins

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Answer

Let the number of small boxes be denoted by $x$ and the number of large boxes be $y$ . We know from the problem that the ratio of the number of tins in small boxes to those in large boxes is 2:3.

Let the number of tins in small boxes be represented as $2k$ and in large boxes as $3k$ . We can calculate as follows:

$2k + 3k = 3000$

This simplifies to:

$5k = 3000 \\ k = 600$

So, the total number of tins in small boxes is $2k = 1200$ and in large boxes is $3k = 1800$ .

Step 2

number of boxes

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Answer

Next, we determine the number of boxes. Given that there are 6 tins in each small box:

Number of small boxes: $\frac{1200}{6} = 200$

And for large boxes, with 20 tins in each box: $\frac{1800}{20} = 90$

Thus, Carlo has 200 small boxes and 90 large boxes.

Step 3

percentage of large boxes

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Answer

Now, we can find the percentage of the total boxes that are large boxes:

Total boxes = $200 + 90 = 290$

Calculating the percentage of large boxes:

$\frac{90}{290} \times 100 \approx 31.03\%$

Since 31.03% is greater than 30%, Carlo's statement is incorrect.

Step 4

conclusion

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Answer

Based on the calculations, Carlo is not correct in stating that less than 30% of the boxes filled with tins are large boxes.

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

total tins

number of boxes

percentage of large boxes

conclusion

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