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13 (a) The mass of flour used in a recipe doubles as the number of biscuits made doubles - OCR - GCSE Maths - Question 13 - 2020 - Paper 3
Question 13
13 (a) The mass of flour used in a recipe doubles as the number of biscuits made doubles. On the axes below, sketch a graph to show this relationship. (b) Here are ... show full transcript
Worked Solution & Example Answer:13 (a) The mass of flour used in a recipe doubles as the number of biscuits made doubles - OCR - GCSE Maths - Question 13 - 2020 - Paper 3
Step 1
The mass of flour used in a recipe doubles as the number of biscuits made doubles.
Answer
To visualize this relationship, you would draw a straight line on a graph. The x-axis represents the number of biscuits, and the y-axis represents the mass of flour in grams. You would start at the origin (0, 0) and plot a line that passes through points like (10, 120) and (20, 240), illustrating that as the number of biscuits doubles, so does the mass of flour used.
Step 2
Find the number of biscuits she made.
Answer
First, calculate the flour needed for 432g of butter. The recipe states that 120g of butter is needed to make 10 biscuits, so to find the relationship of butter to biscuits, we set up a ratio:
If 120g butter makes 10 biscuits, then using the equation:
ext{biscuit ext{s}} = rac{432g ext{ butter}}{120g} imes 10 = 36 ext{ biscuits}
Thus, Jane made 36 biscuits.
Step 3
Find the mass of the sugar, in grams, that Jane has left in the bag.
Answer
Jane initially had a 2 kg bag of sugar, which is equivalent to 2000 grams. Since the recipe calls for 100g of sugar to make 10 biscuits, the requirement for the 36 biscuits she made is:
For 36 biscuits, the sugar required is:
ext{sugar ext{ left}} = 2000g - rac{100g}{10} imes 36 = 2000g - 360g = 1640g
Therefore, Jane has 1640 grams of sugar left in the bag.