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Coffee Mixture Problem (Challenging)?
A coffee merchant mixes two types of beans, bean (1) and bean (2), to make different blends of coffee. All of these blends are sold at the same price.
If he mixes bean (1) and bean (2) in the ratio (by weight) 2 : 1, then he makes a profit of 26%.
If he mixes bean (1) and bean (2) in the ratio (by weight) 3 : 2, then he makes a profit of 20%.
In what ratio should he blend bean (1) and bean (2) for his profit to be 40%?
1 Answer
- M3Lv 77 years agoFavorite Answer
let unit cost price of type 1 be x and that of type 2 be 1, then
(2x + 1)/3 is the unit cost price of 1st mixture, 100/126 of unit sale price
and (3x+2)/5 is the unit price of 2nd mixture, 100/120 of unit sale price
thus unit sale price = (126/100)(2x+1)/3 = (120/100)(3x+2)/5,
which yields x = 1/2
and unit sale price = (126/100)(2/3) = 0.84
let the desired ratio be k:1, then
[k/2 +1]/(1+k) = 100/140 *0.84
which yields k = 4
desired ratio = 4:1
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