Question

a teacher brought to class a pack of notebooks. if her gives his students 5 notebooks to each, he will have 7 notebooks left. if he tries to give each student 7 notebooks, he will be 5 notebooks short. how many students are there in the class?

Answer 1

Answer:

6 students

Step-by-step explanation:

Let the number of notebooks be $x$ and the number of students be $y.$

If there are 5 notebooks per student, we have:

$x-5y=7$

Simliairly, we have 7 notebooks per person, which is:

$x-7y=-5$

Then, using system of equations, we can add multiply the first equation by $-1$ and then add.

We would have:

$-1(x-7y=-5)=-x+7y=5$

Then, adding gives us:

$2y=12$

$y=6$

Answer 2

There are 6 students in the class.

Let x represent the number of students that are there in the class.

The teacher her gives his students 5 notebooks each, and still has 7 notebooks left.

The number of note books = 5x + 7    (1)

The teacher her gives his students 7 notebooks each, and was 5 notebooks short.

The number of note books = 7x - 5   (2)

Therefore equating equations 1 and 2:

5x + 7 = 7x - 5

7x - 5x = 7 + 5

2x = 12

x = 6

There are 6 students in the class.

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