Henry Ernest Dudeney/Puzzles and Curious Problems/301 - Weighing the Tea/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $301$

A grocer proposed to put up $20$ pounds of China tea into $2$-pound packets,

but the weights had been misplaced by somebody, and he could only find the $5$-pound and the $9$-pound weights.

What is the quickest way for him to do the business?

We will say at once that only nine weighings are really necessary.

Having weighed a quantity of tea, we can then use that as a further weight to make further weighings.

We will refer to each weight merely by its numerical weight in pounds for simplicity.

$(1): \quad$ With the $5$-pound weight and the $9$-pound in opposite pans, weigh a $4$-pound weight of tea.

$(2): \quad$ With the $4$-pound weight of tea, weigh another $4$-pound weight of tea.

$(3): \quad$ With the $4$-pound weight of tea, weigh a third $4$-pound weight of tea.

$(4): \quad$ With the $4$-pound weight of tea, weigh a fourth $4$-pound weight of tea.

Note that the remaining tea in the chest will also make a $4$-pound weight of tea.

$(5)$ to $(9): \quad$ Divide each of the $4$-pound weights of tea equally between the two pans of the balance.