Mrs. Mendoza is organizing seating for a standardized test. 45 ninth-grade students and 120 tenth-grade students will take the test. Each row will have the same number of students, but ninth graders and tenth graders will not be seated in the same row. If she puts the greatest possible number of students in each row, how many rows will there be?

Answer: 11 rows

Step-by-step explanation:

This is a case of finding the highest common factor of 45 and 120.

Highest common factor is the largest number possible to divide two or more numbers without remainder, and in this case, the highest possible number to divide 45 and 120 without remainder. This highest common factor will be exactly equal to the number of students in each row.

Putting 45 and 120 on the division table,

Factors

3 ... l[45] l[120]

5 ... l[15] l[40]

... l[3 ] l[8]

From this table, our HCF is the multiplication of the entries under the factor column (3 and 5)

Hence, HCF = 3*5 = 15

each row will have 15 students.

Since ninth and tenth graders will not be put on the same row, then:

For the ninth graders with 45 students, there will be 3 rows

And for the tenth graders with 120 students, there will be 8rows

So in total, we have 3+8 = 11 rows.