Video: AF5P2-Q15-860101529174

Amaya has two fields to keep her pigs and chickens, field A and field B. Each pig needs 3.5 m² of space. Each chicken needs 1.5 m² of space. Amaya does not want to mix the pigs and chickens so she is only going to keep one type of animal in each field. In which field should Amaya keep the pigs and in which field should she keep the chickens In order to maximise the total number of pigs and chickens that she can keep? You must show your working.

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Video Transcript

Amaya has two fields to keep her pigs and chickens, field A and field B. Each pig needs 3.5 square meters of space. Each chicken needs 1.5 square meters of space. Amaya does not want to mix the pigs and chickens. So she is only going to keep one type of animal in each field. In which field should Amaya keep the pigs? And in which field should she keep the chickens In order to maximise the total number of pigs and chickens that she can keep? You must show your working.

There are two possible answers here. Either Amaya keeps pigs in field A and chickens in field B. Or she keeps chickens in field A and pigs in field B. We know from the question that each pig needs 3.5 square meters of space. And each chicken needs 1.5 square meters.

Our first step is to calculate the area of each of the fields. The area of field A can be split into three rectangles and squares. In the top left-hand corner, we have a square, five meters by five meters. In the bottom right corner, we also have an area of five meters by five meters. The middle section is a rectangle with dimensions 10 meters by 15 meters. Five multiplied by five is equal to 25. And 10 multiplied by 15 is equal to 150. This means that the total area of field A can be calculated by adding 25, 25, and 150. This is equal to 200. Therefore, the area of field A is 200 square meters. Field B is a rectangle. Therefore, the area can be calculated by multiplying 12 by 21. This is equal to 252. Therefore, the area of field B is 252 square meters.

We now need to calculate how many pigs and how many chickens we can keep in each of the fields. Let’s firstly consider pigs in field A and chickens in field B. Field A has an area of 200 square meters. And each of the pigs needs 3.5 square meters of space. Therefore, we need to divide 200 by 3.5. This is equal to 57.142 et cetera. As we can’t keep part of an animal, this means that we can keep 57 pigs in field A. The area of field B was 252 square meters. And each chicken needs 1.5 square meters of space. Therefore, we need to divide 252 by 1.5. This is equal to 168. We can keep a total of 168 chickens in field B. 57 plus 168 is equal to 225. Therefore, if Amaya keeps pigs in field A and chickens in field B, she can keep a total of 225 animals.

Let’s now consider the second option where Amaya keeps chickens in field A and pigs in field B. This time, we need to divide 200 by 1.5 to calculate the number of chickens. This is equal to 133.3 recurring. Amaya can keep 133 chickens in field A. The number of pigs that she can keep in field B is calculated by dividing 252 by 3.5. This is equal to 72. Amaya can keep 133 chickens in field A and 72 pigs in field B. This gives us a total of 205 animals as 133 plus 72 is equal to 205. 225 is greater than 205. In order to maximise the number of animals that she can keep, Amaya should keep pigs in field A and chickens in field B.

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