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There are only blue cubes, yellow cubes and green cubes in a bag - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 2

Question 4

There are only blue cubes, yellow cubes and green cubes in a bag. There are twice as many blue cubes as yellow cubes and four times as many green cubes as blue c... show full transcript

Worked Solution & Example Answer:There are only blue cubes, yellow cubes and green cubes in a bag - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 2

Step 1

Set up the relationships based on the given information

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Answer

Let the number of yellow cubes be represented as $y$ . Then, according to the problem:

There are twice as many blue cubes as yellow cubes: $\text{Blue cubes} = 2y$
There are four times as many green cubes as blue cubes: $\text{Green cubes} = 4(2y) = 8y$

Step 2

Calculate the total number of cubes

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Answer

Now, we can find the total number of cubes in the bag by summing the quantities of all three colors:

$\text{Total cubes} = \text{Yellow cubes} + \text{Blue cubes} + \text{Green cubes}$

Substituting in the values we derived:

$\text{Total cubes} = y + 2y + 8y = 11y$

Step 3

Calculate the probability of selecting a yellow cube

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Answer

The probability of selecting a yellow cube can be calculated as follows:

$P(\text{Yellow cube}) = \frac{\text{Number of yellow cubes}}{\text{Total number of cubes}} = \frac{y}{11y} = \frac{1}{11}$

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