Q. 132 - Intermediate Algebra

Question

Margie is planning a lunch banquet. The equation $C=750+42g$ models the relation between the cost in dollars, C, of the banquet and the number of guests, g.

(a) Find the cost if the number of guests is 50.

(b) Find the cost if the number of guests is 100.

(c) Interpret the slope and C-intercept of the equation.

(d) Graph the equation.

Step-by-Step Solution

Answer

(a) Cost is $2850 for 50 guests.

(b) Cost is $4950 for 100 guests.

(c) Slope is 42 and $\left(0,750\right)$ is the C-intercept.

(d) 

Part (a). Step 1. Given information

The given equation is $C=750+42g$.

Part (a). Step 2. Substitute and simplify

• Substitute 50 for g in the given equation and solve for C.

$\begin{array}{rcl}C& =& 750+42\left(50\right)\\ & =& 750+2100\\ & =& 2850\end{array}$

• Cost is $2850 for 50 guests.

Part (b). Step 1. Substitute and simplify

• Substitute 80 for g in the given equation and solve for C.

$\begin{array}{rcl}C& =& 750+42\left(100\right)\\ & =& 750+4200\\ & =& 4950\end{array}$

• Cost is $4950 for 100 guests.

Part (c). Step 1. Determine the slope and C-intercept.

• The given equation is of the form $y=mx+b$ where g in the given equation denotes x and C denotes y. So, the slope is 42.
• Substitute 0 for g in the given equation and obtain the value of C.

$\begin{array}{rcl}C& =& 750+42\left(0\right)\\ & =& 750\end{array}$

• So, $\left(0,750\right)$ is the C-intercept.

Part (d). Step 1. Simplify the slope

• Rewrite $m=42$ in fractional form.

$42=\frac{42}{1}$

Part (d). Step 2. Graph

• From the point $\left(0,750\right)$, go up 42 units and then move 1 units to the right to obtain the second point.

• The second point will be $\left(1,792\right)$.
• Join the obtained points to plot the equation.