Video: AF5P1-Q13-290154537409v2

The ratios for the minimum number of scout leaders required per scout to run two different activities are shown in the table. (a) There are four scout leaders available to take scouts kayaking. What is the maximum number of scouts that can go kayaking? (b) 27 scouts want to practice archery. What is the smallest number of scout leaders required?

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Video Transcript

The ratios for the minimum number of scout leaders required per scout to run two different activities are shown in the table. Kayaking, scout leaders to scouts one to 11. Archery, scout leaders to scouts one to six. Part a) there are four scout leaders available to take scouts kayaking. What is the maximum number of scouts that can go kayaking?

There’s also a part b that we will look at later. The ratios given are for the minimum number of scout leaders required per scout. We can therefore say that the ratio one to 11 means that there’s at least one leader for 11 scouts or at most 11 scouts for every leader.

For the first part of the question, we’re told there’re four scout leaders. And we want to calculate the maximum number of scouts that can go kayaking. The ratio of scout leaders to scouts is one to 11. We know there’re four scout leaders. And one multiplied by four equals four. In ratio questions, whatever we do to one side of the ratio, we must do to the other. Therefore, we need to multiply the number of scouts by four. 11 multiplied by four is equal to 44. This means that the maximum number of scouts that can go kayaking with four scout leaders is 44. The second part of the question says the following.

b) 27 scouts want to practice archery. What is the smallest number of scout leaders required?

We are told that the ratio of scout leaders to scouts for archery is one to six. We need to calculate the number of scout leaders required for 27 scouts. As we have already mentioned with ratio, whatever we do to one side, we must do to the other. Our first step is to work out the multiplier or scale factor that gets us from six to 27. In order to do this, we need to divide 27 by six. This is equal to four remainder three as six multiplied by four is equal to 24. As the remainder was three and the number we were dividing by is six, then 27 divided by six is equal to four and three-sixths. The remainder becomes the numerator. And the divisor becomes the denominator. Three-sixths is the same or equivalent to one-half as three divided by three is one. And six divided by three is two. Four and a half is the same as 4.5. Therefore, we need 4.5 scout leaders for 27 scouts.

Remember we were told that this is the minimum number of scout leaders. And as we can’t have half a scout leader, we need to round this up to five. If 27 scouts want to practice archery, the smallest number of Scout leaders required is five.

An alternative method here would be to use our knowledge of our six times table. We know that we need one scout leader for every six scouts. This means that we would need two scout leaders for 12 scouts as six multiplied by two is 12. We would need three scout leaders for 18 scouts, four scout leaders for 24 scouts, and five scout leaders for 30 scouts. As 27 is greater than 24, four scout leaders would not be enough. Therefore, once again, we have proved that we need five scout leaders for 27 scouts. Those five scout leaders could take up to 30 scouts to practice archery.

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