Answer:
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.
