a teacher gives 7 stickers to each student in the class, she will have 24 stickers left. she is 32 stickers short of giving each student 9 stickers. how many stickers does she have and how many students

Let N=number of stickers,

s=number of students
7s+24=N
9s-32=N
Solve for s and N by comparison.

To solve this problem, let's assign variables to the unknown quantities. Let's say "x" represents the number of stickers the teacher has, and "n" represents the number of students in the class.

According to the given information, if the teacher gives 7 stickers to each student in the class, she will have 24 stickers left. This can be expressed as:

x - 7n = 24 .....(Equation 1)

Similarly, if the teacher gives each student 9 stickers, she will be 32 stickers short. This can be expressed as:

x - 9n = -32 .....(Equation 2)

Now, we have a system of two equations with two unknowns. We can solve this system of equations to find the values of x and n.

One way to solve this is to use the method of substitution. Let's solve Equation 1 for x:

x = 7n + 24

Now, substitute this expression for x in Equation 2:

7n + 24 - 9n = -32

Simplify by combining like terms:

-2n + 24 = -32

Subtract 24 from both sides:

-2n = -56

Divide both sides by -2:

n = 28

Now, we know there are 28 students in the class. We can substitute this value back into Equation 1 to find x:

x - 7 * 28 = 24

x - 196 = 24

Add 196 to both sides:

x = 220

So, the teacher has 220 stickers and there are 28 students in the class.