Market day

On market day I went out with fifty coins in my pocket and a short list: apples, eggs and a bunch of herbs.

Market day: $50$ coins in my pocket, a list of $3$ things: apples, eggs, herbs.

$c_0=50$. list $=\{A,E,H\}$ (apples, eggs, herbs).

Apples were three coins a kilo, and I took two kilos. Eggs were half a coin each, and I took a dozen. Herbs were four coins a bunch, and I took one.

Apples $3$ coins/kg, I took $2$ kg. Eggs $0.5$ coin each, I took $12$. Herbs $4$ coins a bunch, I took $1$.

$p_A=3$/kg, $q_A=2$ kg. $p_E=0.5$, $q_E=12$. $p_H=4$, $q_H=1$.

The apples came to six coins, the eggs to six and the herbs to four: sixteen coins in all. I handed over twenty coins and got four back.

Apples $3\times 2=6$, eggs $0.5\times 12=6$, herbs $4$: total $6+6+4=16$ coins. I paid $20$, change $=20-16=4$.

$\sum pq=3\cdot 2+0.5\cdot 12+4\cdot 1=16$. paid $20\Rightarrow$ change $=4$.

On the way home I passed a stall where the same apples were two coins a kilo. Had I bought there, I would have saved two coins, enough for half a bunch of herbs.

On the way home: a stall with the same apples at $2$ coins/kg. There: $2\times 2=4$, a saving of $6-4=2$ coins $=$ half a bunch of herbs.

$\exists$ stall: $p_A^{\prime }=2\Rightarrow \Delta =(3-2)\cdot 2=2=p_H/2$.

I got home with thirty-four coins, a bag of about three kilos and one lesson: always walk the whole market once before you buy.

Home: $50-16=34$ coins, a bag of $\approx 3$ kg and $1$ lesson: walk the whole market once before buying.

$c_1=50-16=34$, bag $\approx 3$ kg. lesson: look$(\forall$ stall$)\to$ buy.