SOLUTION: Cookies that sell for $3.30/kg are mixed with cookies that sell for $3.95/kg. The mixture sells for $3.56/kg. How many kilograms of each type of cookie are needed to make 30 kg of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Cookies that sell for $3.30/kg are mixed with cookies that sell for $3.95/kg. The mixture sells for $3.56/kg. How many kilograms of each type of cookie are needed to make 30 kg of       Log On


   

Question 1159726: Cookies that sell for $3.30/kg are mixed with cookies that sell for $3.95/kg. The mixture sells for $3.56/kg. How many kilograms of each type of cookie are needed to make 30 kg of the mixture?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
L, the low price or low concentration
H, the high price or high concentration
T, the target price or concentration
v, the amount of the H material
M, the amount of the mixture of H and L

Hv%2BL%28M-v%29=TM
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Hv-Lv%2BML=MT
%28H-L%29v=MT-ML
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29


Your example:
v=30%28%283.56-3.3%29%2F%283.95-3.3%29%29
v=30%280.26%2F0.65%29
highlight%28v=12%29---------kilograms of the $3.95 per kilogram cookies.
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highlight%2818%29----------kg of the $3.3 per kg cookies.

Answer by greenestamps(13216) About Me  (Show Source):
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The ratio in which the two kinds of cookies must be mixed is exactly determined by where the price per kg of the mixture lies between the prices per kg of the two kinds of cookies.

By whatever method you choose, determine that $3.56 is 2/5 of the way from $3.30 to $3.95. (For example, $3.30 to $3.95 is a difference of $0.65; $3.30 to $3.56 is a difference of $0.26; $0.26/$0.65 = 2/5.)

That means the more expensive cookies have to be 2/5 of the mixture; which of course means 3/5 of the mixture is the less expensive cookies.

ANSWER: 3/5 of 30kg, or 18kg, of the $3.30 per kg cookies, the other 12kg of the $3.95 per kg cookies.