White shapes and black shapes are used in a game - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 1

Let the number of white circles be 4y and white squares be 5y. Thus, the total number of white shapes is 4y + 5y = 9y.

Let the number of black circles be 2z and black squares be 5z. Therefore, the total number of black shapes is 2z + 5z = 7z.

We can express the total number of circles as the sum of white and black circles: 4y + 2z. For solving these ratios, we can assume values for x, y, and z. Using the relationships established:

From the ratio of shapes, we can assume x = 1, giving us 3 white shapes and 7 black shapes. Choosing y = 1 gives us 4 white circles, and 5 white squares, summing to 9 for white shapes. Choosing z = 1 gives us 2 black circles, and 5 black squares, summing to 7 for black shapes.

Therefore, the total number of circles is 4 + 2 = 6, and the total number of shapes is 10. Hence, the fraction of shapes that are circles is:

$\frac{6}{10} = \frac{3}{5}$.