Question

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 x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. According to the model, for what price must the combs be sold?
{ y=x/2 y=-0.03(x-95)^2+550

a. $0.03 each
b. $0.50 each
c. $0.95 each
d. $2.00 each

Answer 1

Solution:

The two equations, which are

1. The linear equation models the income, in dollars, from selling x plastic combs is given as

$y=\frac{x}{2}$

2. The quadratic equation models the cost, in dollars, to produce x plastic combs is given as

 $y=-0.03(x-95)^2+550$

Selling price of x, plastic comb$=\frac{x}{2}$

Selling price of one plastic comb$=\frac{y}{x} =\frac{\frac{x}{2}}{x}=\frac{1}{2}$

               = $0.50

So, selling price of each plastic comb= $ 0.50 each→→Option (B)

Answer 2

The price that the combs must be sold is B $0.50.

How to calculate the price?

From the information given, the linear equation modeling the income from selling x plastics will be:

y = x/2

The quadratic equation will be:

y = 0.03(x - 95)² + 550

Therefore, selling one plastic comb will be:

= 0.5x/x

= 0.5

In conclusion, the price that the combs must be sold is $0.50.

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