Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 9

GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 9

04:56

Video Transcript

Two friends want to deliver 27 identical gifts to a children’s home. Each gift has a mass of 3.9 kilograms. Ahmed estimates the total mass by calculating 30 multiplied by four equals 120. Lauren estimates the total mass by calculating 25 multiplied by four is equal to 100. Part a) Whose estimate is closer to the actual total mass of the gifts? Give a reason for your answer.

Both of the friends have rounded the mass of each gift to four kilograms. Therefore, the four will have no impact on whose estimate is closer. Ahmed rounded the number of gifts up from 27 to 30, whereas Lauren rounded down from 27 to 25. The midpoint between 25 and 30 is 27.5. As 27 is less than this, it is closer to 25 than it is to 30. 27 is two away from 25, but it is three away from 30. We can therefore say that Lauren’s estimate is closer to the actual total mass of the gifts, as 27 is closer to 25 than it is to 30.

The second part of the question says the following. The post office charges a cost for each box that is posted. They need to use 12 boxes to send all of the gifts. Part b) Calculate the cost of buying 12 boxes with the given discount.

Our first step is to calculate the cost of the boxes prior to the discount. In order to do this, we need to multiply 12 by four pound 30. We need 12 boxes, and they cost four pound 30 each. One way of calculating 12 multiplied by four pound 30 is to split the 12 into 10 and two. We can then multiply 10 by four pound 30 and two by four pound 30.

10 multiplied by four pound 30 is 43 pound. We move all the digits one place to the left. Two multiplied by four pound 30 is eight pound 60. Two times four is equal to eight, and two times 30 pence is equal to 60 pence. Adding these two answers gives us a total cost of the 12 boxes of 51 pound and 60 pence.

There is a 10 percent discount if you sent five or more boxes. As we’re sending 12, we can apply this 10 percent discount in this case. We need to calculate 10 percent of 51 pound 60. In order to calculate 10 percent of any quantity, we need to divide the quantity by 10, as 10 percent is equal to one tenth. This is an important percentage you need to remember for any non-calculator exam.

Dividing 51 pound 60 by 10 gives us five pound and 16 pence. We move all the digits one place to the right. This means that we have a discount of five pound and 16 pence. The total cost can be calculated by subtracting five pound 16 pence from 51 pounds and 60 pence. One way of calculating this is using a column subtraction sum.

We are unable to subtract six from zero using this method, so we have to go next door and borrow. The six in the tenths column becomes a five, and we end up with ten hundredths. 10 minus six is equal to four. Five minus one is also equal to four. We need to remember to put in the decimal point. Borrowing one from the tens column gives us four in the tens column and 11 in the ones column. 11 minus five is equal to six, and four minus zero is equal to four. This means that 51 pound 60 minus five pound and 16 is equal to 46 pound and 44 pence. The total cost of buying the 12 boxes with the discount is 46 pounds and 44 pence.

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