SOLUTION: Hi I'm really confused with this question... A shopkeeper mixed a herb worth $2.50 a kilogram with another herb worth $3.50 a kilogram. He sold 20 kilograms of the mixture at $2

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Question 834555: Hi I'm really confused with this question...
A shopkeeper mixed a herb worth $2.50 a kilogram with another herb worth $3.50 a kilogram. He sold 20 kilograms of the mixture at $2.80 per kilogram. Find the weights of the two different herbs he mixed together.

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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A shopkeeper mixed a herb worth $2.50 a kilogram with another herb worth $3.50 a kilogram.
He sold 20 kilograms of the mixture at $2.80 per kilogram.\
Find the weights of the two different herbs he mixed together.
:
Let a = amt of $2.50 herbs
Let b = amt of $3.50 herbs
:
Two equations
the weight equation
a + b = 20
or
a = (20-b); use this form for substitution
:
the $ amt equation
2.50a + 3.50b = 2.80(20)
2.50a + 3.50b = 56
Replace a with (20-b)
2.5(20-b) + 3.5b = 56
50 - 2.5b + 3.5b = 56
-2.5b + 3.5b = 56 - 50
b = 6 kg of the 3.50 herb
then
a = 20 - 6
a = 14 kg of the 2.50 herb
:
:
Check the solutions in the $ equation
2.5(14) + 3.5(6) = 2.8(20)
35 + 21 = 56
:
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