SOLUTION: A merchant blends tea that sells for $4.20 a pound with tea that sells for $2.40 a pound to produce 120 lb of a mixture that sells for $3.45 a pound. How many pounds of each type o

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Question 1017152: A merchant blends tea that sells for $4.20 a pound with tea that sells for $2.40 a pound to produce 120 lb of a mixture that sells for $3.45 a pound. How many pounds of each type of tea does the merchant use in the blend?
Answer by ikleyn(52776) About Me  (Show Source):
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A merchant blends tea that sells for $4.20 a pound with tea that sells for $2.40 a pound to produce 120 lb of a mixture
that sells for $3.45 a pound. How many pounds of each type of tea does the merchant use in the blend?
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Let x = the amount of tea for $4.20 the merchant uses in the blend, in lbs.

Then 120-x is the amount of tea for $2.40 the merchant uses in the blend.

The balance equation is

420x + 240*(120-x) = 120*345.

Simplify it:

420x - 240x = 120*345 - 240*120,

180x = 120*(345 - 240),

180x = 120*105,

x = %28120%2A105%29%2F180 = %282%2A105%29%2F3 = 2*35 = 70.

Answer. 70 lbs for $4.20 and 120-70 = 50 lbs for $2.40