A teacher handed out m packs of notebooks. Each pack contained a notebooks. Now the teacher has 13 notebooks left. How many notebooks did the teacher have originally?
The correct answer and explanation is:
To solve this problem, let’s define the variables and set up an equation.
Let:
- mm be the number of packs of notebooks the teacher handed out.
- aa be the number of notebooks in each pack.
- tt be the total number of notebooks the teacher had originally.
The teacher handed out m×am \times a notebooks, because each of the mm packs contained aa notebooks.
After distributing the notebooks, the teacher has 13 notebooks left. This means the total number of notebooks the teacher started with minus the number of notebooks handed out equals 13. We can express this relationship as: t−m×a=13t – m \times a = 13
Now, let’s solve for tt (the total number of notebooks the teacher originally had): t=m×a+13t = m \times a + 13
This equation shows that the total number of notebooks the teacher started with is the number of notebooks distributed (which is m×am \times a) plus the 13 notebooks remaining.
Without knowing the values of mm and aa, we cannot find the exact number of notebooks the teacher originally had, but this equation tells us the relationship between these quantities. If you know how many packs were handed out or how many notebooks were in each pack, you can substitute those values into the equation to find the original number of notebooks.