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
n - 7 s = 24
9 s - n = 32
------------ add
2 s = 56
s = 28 students
n = 9 (28) - 32
n = 220 stickers
dont no awnser
Let's assign variables to the unknowns in the problem:
Let:
S = number of stickers the teacher has
N = number of students in the class
From the information given, we can write two equations:
Equation 1: The teacher gives 7 stickers to each student and has 24 stickers left.
S - 7N = 24
Equation 2: The teacher is 32 stickers short of giving each student 9 stickers.
S - 9N = -32
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using the elimination method:
Multiply Equation 1 by 9 and Equation 2 by 7 to eliminate the S variable:
9*(S - 7N) = 9*24 -> 9S - 63N = 216 (Equation 3)
7*(S - 9N) = 7*(-32) -> 7S - 63N = -224 (Equation 4)
Now subtract Equation 4 from Equation 3:
(9S - 63N) - (7S - 63N) = 216 - (-224)
9S - 63N - 7S + 63N = 216 + 224
2S = 440
S = 220
Substitute the value of S into Equation 1 to find N:
220 - 7N = 24
-7N = 24 - 220
-7N = -196
N = -196 / -7
N = 28
Therefore, the teacher has 220 stickers and there are 28 students in the class.
To find the number of stickers the teacher initially had and the number of students in the class, we can set up a system of equations.
Let's say the number of stickers the teacher initially had is x, and the number of students in the class is y.
From the given information, we know that:
1) If the teacher gives 7 stickers to each student, she will have 24 stickers left.
This can be expressed as: x - 7y = 24.
2) The teacher is 32 stickers short of giving each student 9 stickers.
This can be expressed as: x - 9y = -32.
Now, we have a system of equations:
x - 7y = 24
x - 9y = -32
We can solve this system of equations using the method of substitution or elimination.
Let's use the elimination method to solve the system.
Subtracting the second equation from the first equation:
(x - 7y) - (x - 9y) = 24 - (-32)
-7y + 9y = 24 + 32
2y = 56
y = 56/2
y = 28
Now that we have the value of y, we can substitute it back into any of the original equations to find the value of x.
Let's substitute y = 28 into equation 1:
x - 7(28) = 24
x - 196 = 24
x = 24 + 196
x = 220
Therefore, the teacher initially had 220 stickers, and there are 28 students in the class.