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
Sep 3, 2015

Answer:

I found:
#"brand"_1=192# pounds
#"brand"_2=288# pounds

Explanation:

Call the quantities of the two blends #x_1# and #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