A teacher bought some bookmarks for her students. if she gave each students 3 bookmarks, she would have 21 bookmarks left. if she gave each students 5 bookmarks, she would be short of 53 bookmarks. How many students does the Teacher have?

The teacher have 32 students.

Step-by-step explanation:

Firstly, 'if she gave each students 3 bookmarks, she would have 21 bookmarks left.' This means that 3x + 21 = amount of bookmarks available. Here the x is the number of students.

Then, 'if she gave each students 5 bookmarks, she would be short of 53 bookmarks.' This means that 5x - 53 = amount of bookmarks avalable.

Since both equations all equal to the same quantity, then we know that:

3x + 21 = 5x - 53

Finally, we just need to rearrange the equation to make x the subject.

3x + 21 = 5x - 53

3x = 5x - 53 - 21

3x = 5x - 74

3x - 5x = - 74

- 2x = - 74

- 2x : - 2 = - 74 : - 2

x = 37

Then, just to make sure, we put the number of students into the equations.

3x + 21 = 5x - 53

3 * 37 + 21 = 5 * 37 - 53

111 + 21 = 185 - 53

132 = 132

This means that x does equal to 37.