Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 18

Meera is trying to stack her magazines into boxes. She has 3 identical boxes. The length and width of the magazines are identical to the length and width of the insides of the boxes. Meera plans to stack the magazines into 3 piles and then put the piles into the 3 boxes. Each box has a height of 0.24 m. Each magazine has a thickness of 6 mm. Meera has 125 magazines. Will she be able to fit them all in the three boxes? You must show your working.

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Video Transcript

Meera is trying to stack her magazines into boxes. She has three identical boxes. The length and width of the magazines are identical to the length and width of the insides of the boxes. Meera plans to stack the magazines into three piles and then put the piles into the three boxes. Each box has a height of 0.24 metres. Each magazine has a thickness of six millimetres. Meera has 125 magazines. Will she be able to fit them all in the three boxes? You must show your working.

There is a lot of information in this question. So it is important to read it carefully. We’re told that the length and width of the magazines are identical to the length and width of the insides of the box. This means that only one magazine fits to the base of the box, as shown in the diagram. We need to work out how many magazines can be stacked in each box.

Each box had a height of 0.24 metres. As the thickness of the magazine was given in millimetres, we need to convert 0.24 metres into millimetres. 100 centimetres is equal to one metre. Therefore, to convert 0.24 metres into centimetres, we multiply by 100. Multiplying by 100 moves all the digits two places to the left. Therefore, 0.24 metres is equal to 24 centimetres.

There are 10 millimetres in one centimetre. Therefore, to convert centimetres to millimetres, we need to multiply by 10. 24 multiplied by 10 is equal to 240. Therefore, the height of the box in millimetres is 240.

Each magazine had a thickness of six millimetres. We need to divide 240 by six to work out how many magazines can fit in one box. 24 divided by six is equal to four, as four multiplied by six equals 24. This means that 240 divided by six is equal to 40. Meera can fit 40 magazines into one box.

Meera has three identical boxes. Therefore, to work out the total number of magazines she can fit in the three boxes, we need to multiply 40 by three. Four multiplied by three is equal to 12. This means that 40 multiplied by three is equal to 120. Meera can fit 120 magazines in three boxes.

As Meera has 125 magazines, the answer is no. She cannot fit them all into the three boxes, as she can only fit 120 magazines into the three boxes. In any question like this, it is important that you show your calculations that have led to your conclusion.

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