WEBVTT
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Thomas is unpacking a delivery of 200 boxes from a lorry into a warehouse.
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There are three different box sizes.
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The number of boxes is in the ratio small to medium to large is equal to 12 to five to three.
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Using a forklift, each trip from the lorry to the warehouse and back takes đť‘Ą minutes.
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Thomas can only transport one type of box per trip.
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In one trip, he can transport 24 small boxes, 10 medium boxes, or three large boxes.
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It takes him one and half hours to unload the lorry and return to his truck.
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Work out the value of đť‘Ą.
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Letâ€™s break this question down into three parts.
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Weâ€™ll begin by using the information about the number of boxes and the ratio in which they shared to work out how many of each type of box there are.
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Weâ€™ll then use the information about the number of boxes he can transport per trip to work out how many trips are going to be required for each type of box.
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And weâ€™re looking to work out the value of đť‘Ą.
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Thatâ€™s the time taken for each trip from the lorry to the warehouse and back and thatâ€™s in minutes.
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So our final step is going to be to work out how long one trip takes Letâ€™s begin by working out how many of each type of box there are.
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We know there are 200 boxes and they split in a ratio small to medium to large, 12 to five to three.
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There are two ways that we can divide 200 into the ratio of 12 to five to three.
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Both methods begin with us working out the total number of parts in our ratio thatâ€™s 12 plus five plus three which is 20.
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Our first method is to then share 200 boxes into these 20 parts.
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Thatâ€™s 200 divided by 20 which is equal to 10.
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We then multiply each part of our ratio by this number 10.
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So for the number of small boxes, thatâ€™s 12 multiplied by 10.
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For the number of medium boxes, itâ€™s five multiplied by 10.
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And for the number of large boxes, itâ€™s three multiplied by 10.
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And we can see that we have 120 small boxes, 50 medium boxes, and 30 large boxes.
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And weâ€™ll briefly consider the other method for sharing 200 in the ratio 12 to five to three.
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We know that the total number of parts is 20.
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And out of these, 12 of these parts represent the number of small boxes.
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So that means twelve twentieths of 200 of the boxes are small.
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And in turn, it means five twentieths of the 200 boxes are medium.
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And three twentieths of the 200 boxes are large.
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And since we commonly replaced the word â€śofâ€ť with the multiplication symbol, we can calculate the number of small boxes by working out twelve twentieths multiplied by 200.
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For medium boxes, thatâ€™s five twentieths multiplied by 200 and for large boxes, itâ€™s three twentieths multiplied by 200.
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And once again, we get the same values as before: 120 small boxes, 50 medium boxes, and 30 large boxes.
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And if we want to check our answer is correct, we could add 120, 50, and 30 and check that it gives us 200 the starting number, which indeed does.
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So weâ€™ve completed part one.
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Weâ€™ve worked out how many small boxes, medium boxes, and large boxes there are.
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Next, weâ€™re going to work out how many trips it takes for each type of box.
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Thomas can transport 24 small boxes in one trip.
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We can work out the number of trips is going to take him to transport 120 boxes by dividing 120 by 24.
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Thatâ€™s five and that means he needs five trips to transport all the boxes.
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Weâ€™ll repeat this process for the medium boxes.
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Itâ€™s 10 boxes per trip.
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And there are 50 boxes.
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So weâ€™re going to work out 50 divided by 10 which once again is five.
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So we need five trips to transport all the medium boxes.
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For the large boxes, he can transport three per trip.
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And there are 30 in total.
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So we work out 30 divided by three which is 10.
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He needs 10 trips to transport all the large boxes.
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Five plus five plus 10 is 20.
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Heâ€™s going to take 20 trips in total.
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And weâ€™ve completed step two.
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Weâ€™ve worked out the number of trips it will take him to transport each type of box.
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And for part three, weâ€™re going to use this information to work out how long one trip is.
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Remember thatâ€™s the value of đť‘Ą.
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And đť‘Ą is in minutes.
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So weâ€™ll need to take that into account as we work through this final step.
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It takes him a total of one and a half hours to unload the lorry and return to his truck.
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Thatâ€™s the same as 90 minutes.
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We worked out that he completes 20 trips during that time.
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So if we divide 90 by 20, it will tell us the time taken for one trip.
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90 divided by 20 is 4.5.
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And we can see that the value of đť‘Ą which represents the time taken to complete a trip from the lorry to the warehouse and back is 4.5 or four and a half minutes.