What blend hits a target price?

Question

You blend \6-per-pound coffee with \10-per-pound coffee and want the blend to cost exactly \7 per pound. Solve in your head. In what ratio should you mix the two? Aim: under 10 seconds.

Accepted Answer

Run the lever backwards (this is "alligation"). The target \7 is \1 above the cheap coffee and \3 below the expensive one. Each component's share is proportional to the distance to the opposite end: \frac{	ext{cheap}}{	ext{expensive}} = \frac{10 - 7}{7 - 6} = \frac{3}{1}. So mix 3 parts \6 coffee to 1 part \10 coffee. Check: \frac{3 \cdot 6 + 1 \cdot 10}{4} = \frac{28}{4} = 7. The target sits near the cheap end, so most of the blend must be the cheap bean. Takeaway. To hit a target average, split in the reverse ratio of the distances to each source value: the closer a source is to the targe…

What blend hits a target price?

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