Question

There are 39 students in Ms. Salazar's chemistry class. If Ms. Salazar divides the class into 9 lab groups of 4 or 5 students each, what would be the number of lab groups with 5 students?

Answer 1

3 groups of 5

Step-by-step 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