# Lesson 20

Rational Equations (Part 1)

- Let’s write and solve some rational equations.

### Problem 1

A local office supply store charges $18 to set up their business card printing machine with the design and $0.15 in materials per business card to print. Select **all** equations that could represent an expression for the average cost \(A(x)\) of printing a batch of \(x\) business cards.

\(A(x)=\frac{18+x}{0.15}\)

\(A(x)=\frac{18+0.15x}{x}\)

\(A(x)=\frac{0.15+18x}{x}\)

\(A(x)=\frac{0.15}{18+x}\)

\(A(x)=\frac{18+0.15x}{18+x}\)

\(A(x)=\frac{18}{x}+0.15\)

### Problem 2

The school band is in charge of a new set of uniforms made with a new logo. A local business charges $140 to set up the logo with the design and $0.25 in materials per logo printed. The function \(C(x)=\frac{140+0.25x}{x}\) represents the average cost per logo if \(x\) uniforms are printed by this business.

- What is the average cost per uniform to get the logo printed on 25 uniforms?
- What is the average cost per uniform to get the logo printed on 100 uniforms?
- How many uniforms should be printed to have an average cost of $1 per logo?
- What will happen to the price as the number of uniforms printed increases?

### Problem 3

Two competing sports equipment suppliers sell footballs at different prices. Supplier A charges $85 in shipping, and charges $2.59 per football. Supplier B charges $50 shipping, and charges $4.29 per football. A school wants to buy 40 balls. Which supplier has the lowest average cost per ball?

### Problem 4

What is one point of intersection between the graphs of the functions \(f(x)=(x + 6)(x+2)\) and \(g(x)=x+ 6\)?

\((0, 6)\)

\((\text-1, 5)\)

\((\text-2, 0)\)

\((\text-4,\text-4)\)

### Problem 5

The graph of a polynomial \(f(x)=(5x-3)(x+4)(x+a)\) has \(x\)-intercepts at -4, \(\frac35\), and 6. What is the value of \(a\)?

### Problem 6

The function \(f(x)=\frac{3x-4}{x+6}\) can be rewritten in the form \(f(x)=3+\frac{\text-22}{x+6}\). What is the end behavior of \(y=f(x)\)?