Video: Pack 5 • Paper 3 • Question 4

Pack 5 • Paper 3 • Question 4

01:34

Video Transcript

Poppy is visiting an animal rescue center to rescue two pets: a cat and a dog. At the rescue center, there are 14 different breeds of dog and some breeds of cat. Poppy says, “There are 156 different ways to choose one breed of dog and one breed of cat.” Could Poppy be right? You must show how you got your answer.

We know that the number of ways to choose one breed of dog and one breed of cat is equal to the number of breeds of dog multiplied by the number of breeds of cat. In the question, we’re given that there are 14 different breeds of dog. And Poppy says that there are 156 ways to choose one breed of dog and one breed of cat. So the only piece of information that we don’t have is the number of breeds of cat.

So let’s call the number of breeds of cat 𝑥. And we obtain an equation that 156 is equal to 14 times 𝑥. And we can get this equation in terms of 𝑥 by dividing both sides by 14. So we obtain that 𝑥 is equal to 156 over 14, which is also equal to 78 over seven, or 11.142857 recurring.

However, 𝑥 represents the number of breeds of cat. And so, therefore, 𝑥 has to be an integer. And as we can quite clearly see, here, 𝑥 is not an integer. And so, therefore, we can conclude that Poppy cannot be correct.

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