Answered

The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. The linear equation models the income, in dollars, from selling [tex]x[/tex] plastic combs; the quadratic equation models the cost, in dollars, to produce [tex]x[/tex] plastic combs. According to the model, for what price is each comb being sold?

[tex]\[
\left\{\begin{array}{l}
y=\frac{x}{2} \\
y=-0.03(x-95)^2+550
\end{array}\right.
\][/tex]

A. \[tex]$0.03
B. \$[/tex]0.50
C. \[tex]$0.95
D. \$[/tex]2.00



Answer :

GinnyAnswer
To determine the price at which each comb is being sold, we need to focus on the linear equation that represents the income from selling [tex]\( x \)[/tex] plastic combs. The income is modeled by the equation:

[tex]\[ y = \frac{x}{2} \][/tex]

Here, [tex]\( y \)[/tex] represents the total income from selling [tex]\( x \)[/tex] combs.

The form of the equation [tex]\( y = \frac{x}{2} \)[/tex] implies that the total income [tex]\( y \)[/tex] is half of the number of combs sold [tex]\( x \)[/tex]. This means that for every comb sold, the income generated can be written as:

[tex]\[ \text{Income per comb} = \frac{1}{2} \][/tex]

Since the income represents dollars, we translate this into a dollar amount per comb. Therefore:

[tex]\[ \frac{1}{2} \text{ dollars per comb} = \$0.50 \text{ per comb} \][/tex]

Thus, the price at which each comb is being sold is:

[tex]\[ \boxed{\$0.50} \][/tex]

Other Questions