Grades 3-4 Video Solutions 2020-2020Levels34prob22

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Problem number 22. Several teams came to the summer kangaroo camp. Each team has five or six members. There are 43 people in total. How many teams are at this camp?  A, four, B, six, C, seven, D, eight, E, nine.  There are 43 people at the camp and 43 is not a multiple of five or of six.  We can try solving this problem by finding out at least how many teams there were and at most how many.  We can take the largest number of teams listed, which is nine, and multiply it by the least number of team members, which is five.  We get nine times five, which is 45.  And that's already too many people because we know there are only 43 people. So even if each team had five members, there would be too many people.  And we know that some teams have six members. So nine does not work.  If we start from the other end, we can multiply the smallest listed number of teams, four,  by the biggest number of people listed, which is six. We get at least 24, which is not enough.  If there are six teams, even if each one's had six members, we only have 36 people, which also is not enough.  If there were seven teams, even if each one had six members, that also would not be enough because it's only 42.  So the answer will have to be D, eight.  We can make eight teams work by having five teams with five members each, which is 25, and three teams with six members each.  Which is 18 people. If we do add those up, we get five plus eight is 13.  One plus two is three plus one more is four.  So D is the only answer that works. There are eight teams at the camp.

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