SOLUTION: l2 kinds of coffee were mixed together, a jamaican coffee worth $5.40 a pound and a vanilla bean coffee worth $6.25 a pound. the mixture contained ten pound more than twice as much

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Question 969086: l2 kinds of coffee were mixed together, a jamaican coffee worth $5.40 a pound and a vanilla bean coffee worth $6.25 a pound. the mixture contained ten pound more than twice as much of the jamaican coffee. how much of each kind was used if the value of the mixture was $190.40
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You mean TWO kinds instead of TWELVE kinds.

VARIABLES:
j, how much Jamaican Coffee
v, how much Vanilla Bean Coffee

The description of j and v quantities,
10+2*what, ... the description falls apart.

Continuing to try, the mixture is j+v.
j%2Bv=10%2B2%2Aj, the mixture, IS, ten pounds more, than two times the amount of Jamaican coffee.
Simplify that is some useful way.
j%2Bv-v=10%2B2j-v
j=10%2B2j-v
j-2j=10%2B2j-v-2j
-j=10-v
highlight_green%28j=v-10%29-----we can work with this.

Back to the fundamental two part mixture problem,

cost%2Fmass=price

%28%285.4%29j%2B%286.25%29v%29%2F%28j%2Bv%29=190.4%2F%28j%2Bv%29

%285.4%29j%2B%286.25%29v=190.4 because accounting for cost is really what is best here;

Substitute according to the complicated description part, for j.
highlight_green%28%285.4%29%28v-10%29%2B%286.25%29v=190.4%29
A unsimplified linear equation in just the one variable, v.
...
and you know what to do from that.....?