Question

Reginald is distributing n boxes of paper to the copy rooms in an office building. If he places 6 boxes of paper in each copy room, there are 7 boxes left over. In order to place 7 boxes of paper in each room, he will need 2 more boxes. How many copy rooms are in the office building?​

Answer 1

Answer:

The total number of copy rooms in the building is 9.

Step-by-step explanation:

With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).

From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:

$n = 6 \cdot r + 7$

From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:

$n = 7 \cdot r - 2$

From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:

$6 \cdot r + 7 = 7 \cdot r - 2$

Puting known and unknowns on opposite sides, we get:

$7+2 = (7-6) \cdot r$

Solving we get:

$9 = r$

Therefor the total number of rooms is 9.

Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.

As a reference, the following link is useful:

https://en.wikipedia.org/wiki/System_of_linear_equations