I had a supplier give me a quote last week that seems very strange, can someone help me out? The quote is for IT hardware, but for simplicity (and anonymity) I'll use apples and oranges:
$$\begin{align} 4\mathrm{~apples}+16\mathrm{~oranges} & = 25\mathrm{~dollars}\\ 8\mathrm{~apples}+48\mathrm{~oranges} & = 96\mathrm{~dollars}\end{align}$$
I've tried to explain to him that the pricing can't be correct, as the unit prices are increasing as volumes increase, which is backwards. He says the pricing is accurate.
I'm not sure how to present the data in a meaningful way or what I can extrapolate from the 2 equations. I know the unique solution is $(-5.25,2.875)$, but I'm not sure what to do with that data.
Any ideas?
Your system of equations is meaningless, because you cannot add apples with oranges, much less get dollars as the sum. Let's rewrite your system as $$\begin{align} (4\mathrm{~apples})\cdot x+(16\mathrm{~oranges})\cdot y & = 25\mathrm{~dollars}\\ (8\mathrm{~apples})\cdot x+(48\mathrm{~oranges})\cdot y & = 96\mathrm{~dollars}\end{align}$$ where $\cdot$ means multiplication, $x$ is the unit price of apples (in dollars per apple), and $y$ is the unit price of oranges (in dollars per orange).
Subtract twice the first equation from the second and you will get $y=2.875\mathrm{~dollars/orange}$. Then plugging in this value to one of the original equations yields $x=-5.25\mathrm{~dollars/apple}$.
Now, this means that you pay the supplier 2.875 dollars for each orange you buy, and the supplier pays you 5.25 dollars for each apple you buy. This doesn't make much business sense, so most likely the supplier is in error.