A grocer wishes to blend 2 different coffee brands. he wants to make a blend of 480 pounds to sell at $2.68 a pound. if he uses a blend of coffee worth $2.50 a pound with another blend worth $2.80 a pound, how many pounds of each does he use?

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A grocer wishes to blend 2 different coffee brands. he wants to make a blend of 480 pounds to sell at $2.68 a pound. if he uses a blend of coffee worth $2.50 a pound with another blend worth $2.80 a pound, how many pounds of each does he use?

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Answer 1 · 2015-09-03T20:39:40

I found:
${brand}_{1} = 192$ $"brand"_1=192$ pounds
${brand}_{2} = 288$ $"brand"_2=288$ pounds

Explanation:

Call the quantities of the two blends $x_{1}$ $x_1$ and $x_{2}$ $x_2$ so you get:
${(x_1+x_2=480),(2.50x_1+2.80x_2=2.68*480):}$
solving by substitution you get:
from the first equation:
$x_1=480-x_2$
substitute into the second equation:
$2.50(480-x_2)+2.80x_2=1286.4$
$1200-2.50x_2+2.80x_2=1286.4$
$0.3x_2=86.4$
$x_2=288$ pounds
and so:
$x_1=480-288=192$ pounds

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A grocer wishes to blend 2 different coffee brands. he wants to make a blend of 480 pounds to sell at $2.68 a pound. if he uses a blend of coffee worth $2.50 a pound with another blend worth $2.80 a pound, how many pounds of each does he use?

1 Answer

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