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Jeff is choosing a shrub and a rose tree for his garden - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 3

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Jeff is choosing a shrub and a rose tree for his garden. At the garden centre there are 17 different types of shrubs and some rose trees. Jeff says, "There are 215 ... show full transcript

Worked Solution & Example Answer:Jeff is choosing a shrub and a rose tree for his garden - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 3

Step 1

Process to find number of rose trees

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Answer

To determine if Jeff's statement is correct, we first need to identify the number of choices he has for the rose trees. Jeff claims that there are 215 ways to choose one shrub and one rose tree.

We know that there are 17 different types of shrubs. If we denote the number of types of rose trees as ( x ), then the total number of combinations can be expressed mathematically as:

17×x=21517 \times x = 215

To find ( x ), we can rearrange this equation:

x=21517=12.647x = \frac{215}{17} = 12.647

Since the number of rose tree types must be a whole number, we must round this value. However, rounding to either 12 or 13 does not yield an integer solution.

Step 2

Conclusion

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Answer

It is not possible for the number of rose trees to result in 215 combinations when paired with 17 shrubs. The total number of rose tree types must be an integer, and as we calculated, it cannot be. Therefore, Jeff is not correct in his statement.

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