so, Buttons Etc. sells buttons at $50 + 1.10 for each button, and Logos sells buttons fro $40 + 1.10 for each button.
A)
let's say that "b" is the amount of buttons Crusader Pep Club is going to buy.
let's take a look at a few buttons prices for Buttons Etc.
1 button.................. 50 + 1.10(1)
2 buttons............... 50 + 1.10(2)
3 buttons............... 50 + 1.10(2)
4 buttons............... 50 + 1.10(4)
5 buttons............... 50 + 1.10(5)
b buttons............... 50 + 1.10(b)
let's take a look at the prices at Logos
1 button.................. 40 + 1.10(1)
2 buttons............... 40 + 1.10(2)
3 buttons............... 40 + 1.10(2)
4 buttons............... 40 + 1.10(4)
5 buttons............... 40 + 1.10(5)
b buttons............... 40 + 1.10(b)
B)
when both companies are the same price, the price equation for Buttons Etc equals the price equation for Logos, namely 50+1.10b = 40 + 1.10b.
when does that occur? At how many buttons?
50+1.10b = 40 + 1.10b
10 ≠ 0
from the system of equations, we end up with 10 = 0, which is not true of course 10 ≠ 0, which is another way to say there's no solution to the system, namely, the equations' graphs never touch each other.
if you recall the slope-intercept form, notice, both have the same slope, so the lines are parallel, and the y-intercept differs, so they never touch each other.
so, since there's no solution, the companies Buttons Etc and Logos sales of buttons will never yield the same price, the prices will always differ for the same amount of buttons sold.
