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A recipe for flapjacks uses only oats, butter and syrup, in the ratio 3 : 2 : 1 - OCR - GCSE Maths - Question 11 - 2018 - Paper 1
Question 11
A recipe for flapjacks uses only oats, butter and syrup, in the ratio 3 : 2 : 1. (a) Pirin makes 1.5kg of flapjacks. He uses 600g of butter. Has Pirin followed thi... show full transcript
Worked Solution & Example Answer:A recipe for flapjacks uses only oats, butter and syrup, in the ratio 3 : 2 : 1 - OCR - GCSE Maths - Question 11 - 2018 - Paper 1
Step 1
Has Pirin followed this recipe?
Answer
To determine if Pirin has followed the recipe correctly, we first need to analyze the total weight of the flapjacks he made and the ratio of ingredients.
The total weight of flapjacks made by Pirin is 1.5 kg, which converts to 1500 g. The ratio of oats, butter, and syrup is 3:2:1, indicating that for every 6 parts of the mixture, 3 parts are oats, 2 parts are butter, and 1 part is syrup.
The total parts in the mixture is:
Calculating the weight of butter according to the ratio:
- Butter (2 parts) = ( \frac{2}{6} \times 1500 = 500 g )
- Therefore, the proportion would suggest that using 600 g of butter places Pirin above this amount.
Since he used 600 g, this means:
- Butter in the recipe: 500 g
- Total with butter: 1500 g
- This indicates Pirin did not comply with the original ratio as he exceeds the butter amount specified.
Thus, Pirin has not followed the recipe.
Step 2
Find the mass of oats needed to make 15 of these flapjacks.
Answer
The original recipe states that 200 g of syrup is required for 10 flapjacks. To find out how much syrup is needed for 15 flapjacks, we first determine the proportion:
For 15 flapjacks:
- Syrup needed = ( 15 \times 20 = 300 g )
Now, using the ratio for the ingredients:
- The total ratio parts are 6. Therefore the amount of oats can be calculated as follows:
- Oats (3 parts) out of 6 parts = ( \frac{3}{6} = 0.5 ) of the total mass.
For a total of (10 flapjacks = 200 g syrup) = 1000 g total for 10 flapjacks. For 15 flapjacks:
- Total mass for 15 flapjacks = ( 15 \times 100 = 1500 g)
- The mass of oats needed:
- Oats = ( 0.5 \times 1500 = 750 g )
Thus, the mass of oats needed to make 15 flapjacks is 900 g.