SOLUTION: A merchant blends tea that sells for $3.45 a pound with tea that sells for $2.15 a pound to produce 80 pounds of a mixture that sells for $2.75 a pound. How many pounds of the $3.

Question 178568: A merchant blends tea that sells for $3.45 a pound with tea that sells for $2.15 a pound to produce 80 pounds of a mixture that sells for $2.75 a pound.
How many pounds of the $3.45/lbs of tea does the new mixture contain? And how many pounds of the $2.15/lbs of tea does the new mixture contain?
Found 2 solutions by Mathtut, josmiceli:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively
:
x+y=80....................eq 1
3.45x+2.15y=2.75(80)......eq 2
:
rewrite eq 1 to x=80-y and plug that value into eq 2
:
3.45(80-y)+2.15y=2.75(80)
:
276-3.45y+2.15y=220
:
-1.3y=56
:
pounds of $2.15 tea
:
pounds of $3.45 tea
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the pounds of the more expensive tea needed
Let = the pounds of the less expensive tea needed
given:
(1)
(2) (in cents)
--------------------------
In words, (2) says
(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =
(lbs of mixture x price/lb of mixture)
--------
Multiply both sides of (1) by and then
subtract from (2)

and, from (1)
(1)

36.92 lbs of the $3.45 tea and 43.08 lbs of the $2.15 tea are needed
check answer:
(2)
(2)

OK
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