New curtains

Dear friend, I have made curtains for my window! The window is one hundred and twenty centimetres wide. A curtain looks better if it is gathered, so I made it one and a half times as wide as the window: one hundred and eighty centimetres.

Dear friend, I have made curtains! The window is $120$ cm wide. A gathered curtain looks better, so I used $1.5\times 120=180$ cm.

Dear friend! Window $w$, fullness $k$: $w=120,k=1.5$, so $kw=1.5\times 120=180$.

Then I added six centimetres for the side hems, which makes one hundred and eighty-six centimetres in all. The cloth is only one hundred and forty centimetres wide, so I made two panels, each ninety-three centimetres wide.

Six more centimetres for the hems: $180+6=186$ cm. The cloth is only $140$ cm wide, so two panels of $186÷2=93$ cm each, and $93<140$.

With hems: $180+6=186$; two panels, each $\frac{186}{2}=93<140$ (the cloth width).

For the length I measured one hundred and fifty centimetres from the rail to the sill, and added eight for the bottom hem and four for the top. Each panel is one hundred and sixty-two centimetres long, so two panels need three hundred and twenty-four centimetres of cloth. I bought three and a half metres.

Length: $150$ cm from rail to sill, so $150+8+4=162$ cm for each panel. Two panels: $2\times 162=324$ cm. I bought $3.5$ m, which is $350$ cm.

Length $\ell =150+8+4=162$; cloth $2\ell =324\le 350$.

What was left over? Twenty-six centimetres, the full width of the cloth. It was just enough for a little bag for the clothes pegs. Come and see it soon! With love.

Left over: $350-324=26$ cm, the whole width of the cloth, just enough for a peg bag. Come and see! With love.

Left over: $350-324=26$, a peg bag. With love.