Question

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?

Answer 1

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