Kids on a 45-seat bus(I'm only a Year 7 so please explain clearly how you found the solution.)A bus has 45 seats. Each seat can fit two children or one child with his backpack. If 2 / 3 of the children have backpacks, how many children can be seated on the bus?I started by saying that 45 × 2 = 90 if no one was wearing a backpack. But since 2 / 3 of the kids are, 45 / 3 × 2 = 30 children would need their own seat and 90 − 30 = 60. So I thought 60 children would fit in the bus. Apparently the answer was 54, but why?P.S. I don't know Markdown, so somebody please edit this question

Question

Kids on a   45-seat bus(I&#039;m only a Year   7 so please explain clearly how you found the solution.)A bus has   45 seats. Each seat can fit two children or one child with his backpack. If   2      /    3 of the children have backpacks, how many children can be seated on the bus?I started by saying that   45  ×  2  =  90 if no one was wearing a backpack. But since   2      /    3 of the kids are,   45      /    3  ×  2  =  30 children would need their own seat and   90  −  30  =  60. So I thought   60 children would fit in the bus. Apparently the answer was   54, but why?P.S. I don&#039;t know Markdown, so somebody please edit this question

mooseEredkefet8 · Accepted Answer

Subtracting 30 from 90 means that you&#039;re removing some children from the bus -- but those you are kicking out all have backpacks. Therefore, among those that are left on the bus, those with backpacks are more than two thirds.In other words, you now have a bus with 30 kids without backpacks and 30 kids with -- and those 60 kids do excatly fill out all the seats, but now only half of them have backpacks.A better way to proceed would be to note that every group of three children (two with backpacks, one without) will need   2      1    2   seats, which is   5 half-seats. There are   90 half-seats in the bus, so there must be       90    5    =  18 groups of   3 children, for a total of   18  ×  3  =  54 children.

Katelyn Reyes · Accepted Answer

If you know basic equations, here&#039;s my explanation:Let   N be the number of children we want to know.Then we know, that 2/3 of then (i.e. 2N/3) need their own seat. The rest of them (N/3) needs only half a seat (since two children fit on one seat). So, we have  45  =      2    3    N  ⋅  1  +      1    3    N  ⋅      1    2  If we summarize, we get  45  =      5    6    NAnd hence   N  =      6    5    ⋅  45  =  54

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