The cost of a company picnic varies directly as the number of employees attending the picnic. if a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees? answer asap

The company picnic cost $ 1300 for 80 employees

Solution:

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

How much does a company picnic cost for 80 employees?

Substitute n = 80 and k = 16.25 in eqn 1

Thus $ 1300 is the cost for 80 employees

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:

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !