SOLUTION: A merchant blends tea that sells for $3.45 a lb. with tea that sells for $1.75 a lb. to produce 70 lb. of a mixture that sells for $2.75 a lb. Contains ? of the $3.45 a lb ? $1

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Question 124265: A merchant blends tea that sells for $3.45 a lb. with tea that sells for $1.75 a lb. to produce 70 lb. of a mixture that sells for $2.75 a lb.
Contains
? of the $3.45 a lb
? $1.75 a lb.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It is given that there will be 70 lb of mixture of the teas
Also given is that the mixture will sell for $2.75 / lb.
Let a = lbs of $3.45 tea
Let b = lbs of $1.75 tea
Since a and b account for the whole mixture,
a+%2B+b+=+70
multiply both sides by -1.75
(1)-a%2A1.75+-+b%2A1.75+=+-122.5
%28a%2A3.45%29+%2B+%28b%2A1.75%29+=+70%2A2.75
(2)%28a%2A3.45%29+%2B+%28b%2A1.75%29+=+192.5
Add (1) and (2)
a%2A1.7+=+70
a+=+41.176
b+=+70+-+41.176
b+=+28.823
check
(1)-a%2A1.75+-+b%2A1.75+=+-122.5
%28a%2A3.45%29+%2B+%28b%2A1.75%29+=+70%2A2.75
41.176%2A3.45+%2B+28.823%2A1.75+=+70%2A2.75
142.057+%2B+50.44+=+192.5
192.497+=+192.5 close enough
So, I get 41.176 lbs of the $3.45 tea and
28.823lbs of the $1.75 tea