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 Ratio: 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

To find out how much sand Bob buys, we first need to determine the total weight of the dry concrete he is making for 50 bags:

Each bag weighs 30 kg, so:

$50 ext{ bags} imes 30 ext{ kg/bag} = 1500 ext{ kg}$

Next, we use the mixing ratio of cement:sand:stone, which is 1:2:3. The total parts in the mixture are:

Total parts = 1 + 2 + 3 = 6 parts

Now, let's calculate the weight of each component:

Weight of sand:

$ext{Weight of sand} = rac{2 ext{ parts}}{6 ext{ parts}} imes 1500 ext{ kg} = 500 ext{ kg}$

Thus, Bob buys 500 kg of sand as shown.

Step 2

Calculate Bob's percentage profit.

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Answer

To calculate Bob's percentage profit, we need to first determine the total cost of buying the ingredients and then compare it to his total sales revenue.

Calculate the cost of cement, sand, and stone:
- Cement: 25 kg at £5.50/bag x 2 bags = £11.00
- Sand: 20 kg at £2.00/bag x 25 bags = £50.00
- Stone: 15 kg at £3.90/bag x 10 bags = £39.00
Total cost:

$£11.00 + £50.00 + £39.00 = £100.00$
Bob sells the 50 bags of dry concrete for £396.
Calculate profit:

Profit = Total revenue - Total cost:

$Profit = £396 - £100 = £296$
Finally, calculate the percentage profit:

$ext{Percentage Profit} = rac{ ext{Profit}}{ ext{Total Cost}} imes 100$

$ext{Percentage Profit} = rac{£296}{£100} imes 100 = 296 ext{%}$

Thus, Bob's percentage profit is 296%.

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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