The audio-visual technician for a hotel ordered 4 boxes of microphone cords. there are 12 cords in each box. if there are now a total of 108 cords at the hotel, how many boxes of cords were there before the order?

 5 boxes.

Step-by-step explanation:

Given : The audio-visual technician for a hotel ordered 4 boxes of microphone cords.

There are 12 cords in each box.

Then, the number of cords in 4 boxes will be

If there are now a total of 108 cords at the hotel,  then the number of corfds were before the order : 108-48=60

Then, the number of boxes were in hotel before the order :-

Hence, there were 5 boxes of cords in the hotel before the order.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: