Question

A manager of a venue sets up 15 large tables and
x
x small tables to seat guests for a particular event. The large tables seat 6 guests each and the small tables seat 4 guests each.



Suppose every table set up for the event is full and the function
f
(
x
)
=
90
+
4
x
f(x)=90+4x represents the total number of guests seated at the venue.



Determine the value of
f
(
16
)
f(16)



f
(
16
)
=
f(16)=

(b)
What is the meaning of
?

A
The total number of people sitting at small tables

B
The total number of guests and tables

C
The total number of tables set up when there are 16 guests

D
The total number of guests at the event when there are 16 tables set up

Answer 1

To determine the value of \( f(16) \) given the function \( f(x) = 90 + 4x \):

Plug \( x = 16 \) into the function:

\[
f(16) = 90 + 4(16)
\]

Calculate \( 4(16) \):

\[
4(16) = 64
\]

Now, combine that with 90:

\[
f(16) = 90 + 64 = 154
\]

So,

\[
f(16) = 154
\]

---

(b) Now, let's analyze the meaning of \( f(16) \).

The function \( f(x) \) represents the total number of guests seated at the venue when there are \( x \) small tables, along with 15 large tables.

When \( x = 16 \), \( f(16) \) gives us the total number of guests seated when there are 16 small tables and the 15 large tables that always seat 6 guests each.

Thus, \( f(16) = 154 \) represents the total number of guests at the event when there are 16 small tables set up.

So, the correct interpretation is:

**D. The total number of guests at the event when there are 16 tables set up.**