SOLUTION: An owner of a gourmet food store has two varieties of herbal teas, one that costs $4 per kilogram and another that costs $5 per kilogram. How many kilograms of each type are needed
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Question 164100: An owner of a gourmet food store has two varieties of herbal teas, one that costs $4 per kilogram and another that costs $5 per kilogram. How many kilograms of each type are needed to make 20 kg of a blend worth $4.60 per kilogram? Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=number of kilos needed of the $4 tea
Then 20-x=number of kilos needed of the $5 tea
Now we know that the value of the tea before it's mixed has to equal the value of the tea after it's mixed, ok?
Value of the tea before it's mixed ($ understood)=4x+5(20-x)
Value of the tea after it's mixed=4.60*20=92
So, our equation to solve is:
4x+5(20-x)=92 get rid of parens (distributive law)
4x+100-5x=92 subtract 100 from each side
4x+100-100-5x=92-100 collect like terms
-x=-8 multiply each side by -1
x=8 kilos---------------------------------amount of $4 tea needed
20-x=20-8=12 kilos---------------------------amount of $5 tea needed
CK
4*8+5*12=4.60*20
32+60=92
92=92
Hope this helps------ptaylor
