A letter to a neighbour

Dear neighbour, thank you for lending me your drill for three days. My shelves are straight at last.

Dear neighbour, thank you for lending me your drill for $3$ days. My shelves are straight.

Thank you: borrowed $d=3$ days.

I had thought of buying one, which costs sixty tokens. If I paid two tokens a day to borrow instead, I would have to borrow for thirty days before buying became cheaper. I need a drill about six days a year, so borrowing costs me only twelve tokens a year.

Buying costs $60$ tokens; borrowing costs $2$ a day, so they break even at $\frac{60}{2}=30$ days. I need $6$ days a year, and $6\times 2=12<60$.

Buy $60$, borrow $2d$; break-even: $2d=60\Rightarrow d=30$. For me $d=6$ and $2\cdot 6=12<60$.

Now I have an idea: ten of our neighbouring families each put one tool on a shared shelf. Each family gives only one tool, yet each has ten tools to use.

Ten families, each putting $1$ tool on a shared shelf: $10\times 1=10$ tools for every family to use.

$10\cdot 1=10$ tools for each family.

If you agree, I will write ten names on one sheet. Your neighbour.

If you agree, I will write $10$ names on one sheet. Your neighbour.

$10$ names, one sheet. Your neighbour.