Sorting Stella's schoolbus

Let the number of rows with exactly 1 student be $n$ . Hence the number of rows with 2 students will be $25-n$ .

We can write a linear equation: $n+(2)(25-n) = 38 \Rightarrow n=12$ . Therefore $\fbox{12}$ rows would have exactly 1 student in them.

Let x be a row of seats that is occupied by one student

Let y be a row of seats that is occupied by two students

x + y = 25

x + 2y = 38

By elimination, we get,

y = 13 and x = 12

If each row occupied by 1 student, we have $38-25=13$ students left to assign seats to. So we know that 13 rows will have 2 students occupying the row. Therefore the number of rows that have exactly 1 student in them is $25-13=\boxed{12}$

rows = 25 seats = 2 so total seats = 2*25 = 50 sol = 50 - 38 = 12

There are 25 rows with 2 seats each therefore there are 50 seats in total. There are 38 students, so there must be 50 - 38 = 12 seats empty. Since there are no empty rows, each row with an empty seat must have exactly 1 student in it. Therefore there are 12 rows with exactly 1 student in them.

25(2)=38+x , 50-38=x ,
x=12

If one student were to occupy each row, there would be 25 students with seats. Subtract the 25 students from the total of 38 students, to find the students that would not have seats.

$38-25=13$

The remaining 13 students will need to sit in the other seat available in the 25 rows, so 13 rows will be occupied by multiple students. Subtract 13 from 25 to find the remaining rows with 1 student in them.

$25-13=12$

So there are 12 rows of seats with exactly 1 student in them.

      -Or- (This works since there are only 2 seats per row.)

Find the total number of seats available by multiplying the 25 rows by the 2 seats available per row.

$25*2=50$

Divide the total number of seats by the total number of students, the quotient should be left in terms of a whole number and a remainder. The remainder will be the number of rows with only 1 student in them.

$50/38=1 R12$

There are 12 rows of seats with 1 student in them.

Each row has at least one student. This would leave 13 students left over after you subtract 25 single sitting students from the original 38. This would mean 13 students are left to sit with one of the single sitting students. Now 13 rows contain 2 students leaving 12 out of the 25 rows with single sitting students.

Lets solve it analytically without delving deep into mathematical calculations. Imagine a bus which has 25 rows one behind the other. 38 students are getting into the bus one by one. Each would like to get hold of a seat by the window side! Hence, of the first 25, each occupy the window side of the 25 rows of seats. Hence, there are no empty seats left. The first condition is thus fulfilled. Now there are still 13 students remaining who are to seat by their mates and in the end you still have 12 rows of seats which have exactly one sitting.

First you would multiply 25 * 2 which equal 50. Then you would subtract the 38 students and it would give you 12 seat with 1 person in them.