Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight. He buys the cement, sand and stone in bags as shown in this table. | Weight of bag (kg) | Cost per bag (£) | |-------------------|------------------| | Cement | 25 | 5.50 | | Sand | 20 | 2.00 | | Stone | 15 | 3.90 | He packs the dry concrete into 30 kg bags. Bob buys just enough cement, sand and stone to make 50 bags of dry concrete. (a) Show that Bob buys 500 kg of sand. (b) Bob sells the 50 bags of dry concrete for a total of £396. Calculate Bob's percentage profit.

GCSE OCR Maths Proportion: Bob makes dry concrete by mixing

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Question 18

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight. He buys the cement, sand and stone in bags as shown in this table. | Weigh... show full transcript

Worked Solution & Example Answer:Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Step 1

Show that Bob buys 500 kg of sand.

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Answer

The ratio of cement, sand, and stone is 1:2:3. Let's denote the amount of each material purchased:

Cement: $1x$
Sand: $2x$
Stone: $3x$

The total weight of the mixture is:

$1x + 2x + 3x = 6x$

To make 50 bags of 30 kg dry concrete, the total weight required is:

$50 imes 30 = 1500 ext{ kg}$

Setting the total weight equal to 1500 kg, we have:

$6x = 1500$

Solving for $x$ gives:

$x = \frac{1500}{6} = 250$

Now, substituting $x$ back in:

Amount of sand = $2x = 2 imes 250 = 500 ext{ kg}$

Hence, Bob buys 500 kg of sand.

Step 2

Calculate Bob's percentage profit.

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Answer

To find the percentage profit, we first need to determine the total cost and then the profit.

Calculate the total cost of materials:
- Cement: $25 × 5.50 = £137.50$ (for 1 bag)
- Sand: $20 × 2.00 = £40.00$ (for 1 bag)
- Stone: $15 × 3.90 = £58.50$ (for 1 bag)

Total cost for one bag of each:

Total Cost = £137.50 + £40.00 + £58.50 = £236.00

Calculate the cost for the total amount needed:
- Assuming one bag of each (cement, sand, stone), and since he needs more sand (500 kg), the cost will be calculated according to the bags he purchases for sand which totals to more than just one bag as the weight increases.
Selling Price:
- Bob sells 50 bags for a total of £396.
Calculate Profit:
- Profit = Selling Price - Total Cost
- Profit = £396 - Total Cost (add up costs accurately)
Calculate Percentage Profit:
- Percentage Profit = ( \frac{Profit}{Total Cost} \times 100 %) \n This formula will lead us to determine the overall profit percentage Bob made on his sales.

Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Worked Solution & Example Answer:Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1

Show that Bob buys 500 kg of sand.

Calculate Bob's percentage profit.

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