Answer :
We have been given that
It will cost $16 to host 4 attendees
To find the maximum number of attendees that fit into his $20 budget.
Step 1: Obtain the relationship
Since the relationship is directly proportional
If
C represents cost
and A represents attendees,
then mathematically, we can represent the relationship as follow
[tex]\begin{gathered} C=\text{ kA} \\ \text{where k is constant} \\ k=\frac{C}{A} \end{gathered}[/tex]When c= $16 and a=4
The value of the constant will be
[tex]k=\frac{16}{4}=4[/tex]Hence the relationship is
[tex]C=4A[/tex]Step 2: Find the number of attendees that will fit into the $20 budget
In this case, we will find A
[tex]\begin{gathered} A=\frac{C}{4} \\ where\text{ C = 20} \\ A=\frac{20}{4} \\ \\ A=5\text{ attend}ees \end{gathered}[/tex]Answer = 5 attendees