Question

1.copy each of these shapes onto squared paper.( draw in ur graph paper) enlarge each one using the given scale factors and centres of enlargement. (5) 2. (4) the pie charts show the results of a survey about the type of chocolate preferred by men and by women. 480 men took part in the survey. 600 women took part in the survey. a how many men chose plain chocolate? b how many women chose plain chocolate? c hassan thinks that more men than women like milk chocolate. is hassan correct? show how you worked out your answer. d the caramel sector for men and women is the same size. without doing any calculations, explain how you know that more women than men chose caramel.

Explanation:

Step1: Solve part 1

Draw the given shape on squared - paper and then for each vertex of the shape, multiply the coordinates (if considering a coordinate - based approach) by the scale factor 3 with respect to the given centre of enlargement. Since the centre of enlargement is not specified in the problem statement, assume it is the origin for simplicity. If the vertices of the original shape are \((x,y)\), the new vertices after enlargement with a scale factor of 3 will be \((3x,3y)\).

Step2: Solve part 2a

The total number of men is \(n_m = 480\). The angle for plain chocolate in the men's pie - chart is \(135^{\circ}\). The proportion of men who chose plain chocolate is \(\frac{135}{360}\). So the number of men who chose plain chocolate is \(480\times\frac{135}{360}=180\).

Step3: Solve part 2b

The total number of women is \(n_w = 600\). The angle for plain chocolate in the women's pie - chart is \(81^{\circ}\). The proportion of women who chose plain chocolate is \(\frac{81}{360}\). So the number of women who chose plain chocolate is \(600\times\frac{81}{360}=135\).

Step4: Solve part 2c

The angle for milk chocolate in the men's pie - chart is \(120^{\circ}\), so the number of men who chose milk chocolate is \(480\times\frac{120}{360}=160\). The angle for milk chocolate in the women's pie - chart is \(120^{\circ}\), so the number of women who chose milk chocolate is \(600\times\frac{120}{360}=200\). Since \(200>160\), more women than men like milk chocolate, so Hassan is incorrect.

Step5: Solve part 2d

In the men's pie - chart, the angle for caramel is smaller than the angle for caramel in the women's pie - chart. Since the total number of women (\(600\)) is greater than the total number of men (\(480\)) and the proportion of women for caramel (judging by the angle in the pie - chart) is larger than that of men, more women than men chose caramel.

Answer:

1. Draw the enlarged shape on squared paper as described in Step1.

2a. 180 men chose plain chocolate.
2b. 135 women chose plain chocolate.
2c. Hassan is incorrect.
2d. More women than men chose caramel because the angle for caramel in the women's pie - chart is larger and the total number of women is greater than the total number of men.