Answer:
3 groups of 5
Explanation:
if x is the number of groups of four, and y is the number of groups of five, then 4x +5y =39 (four students per group of four times the # of groups of four, and 5 students per group times the # of groups of five, which should equal the total amount of students, 39). also, x+y=9. (number of each type of group = 9 groups total).
then, use these two equations and solve for y, by "canceling out" x. there are many ways to do this, but i'm going to use subtraction.
4x-5y=39
x+y=9
you want to change the equation
x+y=9
into
4x+4y=36
by multiplying the whole equation by four. because in order to cancel out the x, you need it to equal zero. in the first equation, its 4x.
so its now
4x-5y =39 MINUS
4x+4y=36
___________
y=3
you can check your work because the remaining 6 groups of four (24 total students) plus the 3 groups of five (15 total students) adds up to equal 36
