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White shapes and black shapes are used in a game - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 1
Question 14
White shapes and black shapes are used in a game. Some of the shapes are circles. All the other shapes are squares. The ratio of the number of white shapes to the n... show full transcript
Worked Solution & Example Answer:White shapes and black shapes are used in a game - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 1
Step 1
Step 2
The ratio of the number of white circles to the number of white squares is 4:5
Answer
Let the number of white circles be 4y and the number of white squares be 5y. Since the total number of white shapes is 3x, we can express this as:
Thus, we find that ( x = 3y ). The number of white circles is: ( 4y ) and the number of white squares is: ( 5y ).
Step 3
The ratio of the number of black circles to the number of black squares is 2:5
Answer
Let the number of black circles be 2z and the number of black squares be 5z. The total number of black shapes is:
Substituting ( x = 3y ), we get:
Thus, we find that ( z = 3y ). The number of black circles is: ( 2z = 6y ) and the number of black squares is: ( 5z = 15y ).
Step 4
Work out what fraction of all the shapes are circles.
Answer
Now, we can calculate the total number of shapes:
Total white shapes: ( 3x = 9y ) Total black shapes: ( 7x = 21y )
Total shapes = ( 9y + 21y = 30y )
Total circles = ( 4y + 6y = 10y )
Hence, the fraction of shapes that are circles is:
Thus, the fraction of all the shapes that are circles is ( \frac{1}{3} ).