Question 354203
You are on the right track...sort of!
Let x = the number of lbs of the $3.00-tea, then (80-x) = the number of lbs of the $2.75-tea. The sum of these two amounts (x+(80-x)) are to equal 80 lbs of $2.90-tea blend. So we can set up the necessary equation to find x.
$3.00(x)+$2.75(80-x) = $2.90(80) We'll drop the $ sign for convenience.
3x+2.75(80-x) = 2.9(80) Simplify.
3x+220-2.75x = 232 Combine like-terms.
0.25x+220 = 232 Subtract 220 from both sides.
0.25x = 12 Divide both sides by 0.25
x = 48 and 80-x = 32
The merchant will need to mix 48 lbs of the $3.00-tea with 32 lbs of the $2.75-tea to obtain 80 lbs of $2.90 tea blend.