There are four types of cards in a game - Edexcel - GCSE Maths - Question 3 - 2020 - Paper 1
Question 3
There are four types of cards in a game.
Each card has a black circle or a white circle or a black triangle or a white triangle.
- number of cards with a black sha... show full transcript
Worked Solution & Example Answer:There are four types of cards in a game - Edexcel - GCSE Maths - Question 3 - 2020 - Paper 1
Step 1
number of cards with a black shape and a circle
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Answer
Let the number of cards that have a black shape be represented by 3x and that with a white shape by 5x (from the ratio of black to white shapes). Thus, the total number of cards is:
extTotalcards=3x+5x=8x
Step 2
number of cards with a white shape and a triangle
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Answer
Similarly, let the number of cards with a white shape (triangles) be represented as 2y and that with a black shape (triangles) by 7y. Thus, the total number of cards with triangles is:
extTotalcardswithtriangles=2y+7y=9y
Step 3
Expressing the answer
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Answer
To find the black shapes as a fraction of the total number of cards with a triangle, we can set 8x and 9y to equal:
If we equate the total number of cards (i.e., both expressions represent the total), we can set up a ratio. Thus,
rac{3x}{9y},
Now substituting an equivalent value for the total number of cards that allows for eliminating y, we can substitute the values:
This leads to the answer: rac{27}{56} as the simplified fraction.
