Thread: Finding the total

Monday: 25 students absent
Tuesday: 20 students absent
Wednesday: 10 students absent
Thursday: 15 students absent
Friday: 20 students absent

Of the given above absences, 8 students were absent exactly 2 days each, 1 was absent 3 days, and no students were absent more than 3 days. If 5 percent of the students in the school were absent at least 1 day last week, how many students are enrolled in this school?

How can it be 1600??

There are a total of 90 reported absences for the week. To find how many students this involves, we subtract the 8 that are counted twice, and 2 for the one student that was counted 3 times. This means 90 - (8 + 2) = 80 students were involved in the absences. So, we are left with 80 is 5% of what number. Since 5% is 1/20, we find the number of students in the school is 20·80 = 1600.

I'm still rather lost, the last couple of sentences do not make sense to me Maybe if we could solve it more algebraically?

80 = x/20

1600 = x

Why do we subtract 2? What about the "2 days each" "3 days" "at least 1 day". These seem to be throwing me off as to why the solution is the way it is.

We subtract 1 for each person absent twice because each person has two absences associated with them in the total of 90, but only represent one person each. For the person absent 3 times, there are 3 absences associated with them, so we need to subtract 2 so that we only count them once.