Rational Equations/Inequalities 1. The average cost function $$ a(x)=\frac{x^{2}-5 x+8}{x} $$ gives the average cost of producing $$ x $$ tool kits. How many tool kits must be produced in order for the average cost to be $$ \$ 4 $$ per tool kit?

Question

UpStudy AI · Accepted Answer

1. We are given the average cost function 
   $$
   a(x)=\frac{x^2-5x+8}{x},
   $$
   and we need to find $$ x $$ such that 
   $$
   a(x)=4.
   $$

2. Set up the equation:
   $$
   \frac{x^2-5x+8}{x}=4.
   $$

3. Multiply both sides of the equation by $$ x $$ (assuming $$ x\neq 0 $$):
   $$
   x^2-5x+8=4x.
   $$

4. Rearrange the equation to set it to zero:
   $$
   x^2-5x+8-4x=0 \quad \Longrightarrow \quad x^2-9x+8=0.
   $$

5. Factor the quadratic equation:
   $$
   (x-1)(x-8)=0.
   $$

6. Solve for $$ x $$:
   $$
   x=1 \quad \text{or} \quad x=8.
   $$

7. Both values are valid since $$ x \neq 0 $$.

Thus, the number of tool kits must be either $$ x=1 $$ or $$ x=8 $$ in order for the average cost to be $$ \$4 $$ per tool kit.
To find the number of tool kits where the average cost is \$4, set up the equation $$ \frac{x^2 - 5x + 8}{x} = 4 $$. Solving this gives $$ x = 1 $$ or $$ x = 8 $$. So, producing either 1 or 8 tool kits results in an average cost of \$4 per kit.

Rational Equations/Inequalities

The average cost function gives the average cost of producing tool kits. How
many tool kits must be produced in order for the average cost to be per tool kit?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions

Rational Equations/Inequalities The average cost function gives the average cost of producing tool kits. How many tool kits must be produced in order for the average cost to be per tool kit?