Mixing Teas for Profit: A 25% Return

[splodge1]

A tea importer mixes tea bought at £5.20/kg with tea at £5.60/kg. He sells this blend at £6.80/kg making a profit of 25% on his cost price. In what ratio does he mix the teas?

 

[MarkFL]

Hello and welcome to MHB, splodge! :D

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[MarkFL]

Let's let $T_1$ be the amount of the less expensive tea in a kg of the mix and $T_2$ be the amount of the more expensive tea in a kg of the mix. So right away, we know:

\(\displaystyle T_1+T_2=1\tag{1}\)

Now, if the seller is making a 25% profit, then his cost is \(\displaystyle \frac{4}{5}\) of the selling price, and so we may write:

\(\displaystyle 5.2T_1+5.6T_2=0.8\cdot6.8=5.44\)

Multiplying through by 12.5, we have

\(\displaystyle 65T_1+70T_2=68\tag{2}\)

Multiplying (1) by 65 and then subtracting it from (2), we get:

\(\displaystyle 5T_2=3\implies T_2=\frac{3}{5}\implies T_1=\frac{2}{5}\)

And so we find:

\(\displaystyle T_1:T_2=2:3\)