Henry Ernest Dudeney/Puzzles and Curious Problems/295 - Blending the Teas/Solution

by : $295$

 * Blending the Teas

Solution

 * $70$ pounds of cheaper tea and $30$ pounds of the more expensive one.

Proof
To simplify the analysis, we express all prices in pence:


 * $2 \shillings 8 \oldpence$ per pound is $2 \times 12 + 8 = 32 \oldpence$ per pound
 * $3 \shillings 4 \oldpence$ per pound is $3 \times 12 + 4 = 40 \oldpence$ per pound
 * $3 \shillings 7 \oldpence$ per pound is $3 \times 12 + 7 = 43 \oldpence$ per pound


 * $25 \%$ profit on $32 \oldpence$ per pound is $8 \oldpence$, hence the cheaper brand will be selling at $40 \oldpence$ per pound
 * $25 \%$ profit on $40 \oldpence$ per pound is $10 \oldpence$, hence the dearer brand will be selling at $50 \oldpence$ per pound.

Let $a$ be the weight of cheaper tea going into making the blend.

Let $b$ be the weight of dearer tea going into making the blend.

We have: