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

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
RELATED QUESTIONS
1. An owner of a gourmet food store has two varities of herbal tea, one that cost costs... (answered by ankor@dixie-net.com)

A special tea blend is made from two varieties of herbal tea, one that costs $4.00/kg and (answered by checkley77)

A grocer has 2 kinds of nuts, one that costs $5 per kilogram and another that costs $5.40 (answered by checkley77)

A special coffee blend is made from two varieties of brew, one that costs $4.00/lb and... (answered by ankor@dixie-net.com)

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs... (answered by josgarithmetic)

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs... (answered by mananth,josgarithmetic)

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs... (answered by josgarithmetic)

A grocery store offers a cheese sampler that includes a pepper cheddar cheese that costs... (answered by josgarithmetic,greenestamps)