SOLUTION: To make a mixture of 80 pounds of coffee worth $272 a grocer mixes coffee worth $3.25 a pound with coffee worth $3.25 a pound with coffee worth $3.85 a pound .How many pounds of th

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Question 1062399: To make a mixture of 80 pounds of coffee worth $272 a grocer mixes coffee worth $3.25 a pound with coffee worth $3.25 a pound with coffee worth $3.85 a pound .How many pounds of the cheaper coffee should the grocer use. txt book answer is 60lb
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You want to learn to solve any general coffee mix problem as if like :
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To make a mixture of M pounds of coffee worth $T a grocer mixes coffee worth $L a pound with coffee worth $H a pound .How many pounds of the cheaper coffee should the grocer use? (Assumes that L%3CH).
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Account for the amount of mixture:
Let u be quantity of the lower priced coffee
Let v be quantity of the higher priced coffee
u%2Bv=M

Account for the cost of the mixture:
uL%2BvH=T

Linear System of Equations in Unknowns v and u:
system%28u%2Bv=M%2Cand%2CuL%2BvH=T%29

Solve the system for u and v.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

To make a mixture of 80 pounds of coffee worth $272 a grocer mixes coffee worth $3.25 a pound with coffee worth $3.25 a pound with coffee worth $3.85 a pound .How many pounds of the cheaper coffee should the grocer use. txt book answer is 60lb
Let amount of the cheaper ($3.25 per lb) coffee to mix, be T

Then amount of the more expensive ($3.85) coffee to mix = 80 - T

We then get the following MIXTURE equation: 3.25T + 3.85(80 - T) = 272

3.25T + 308 - 3.85T = 272

3.25T - 3.85T = 272 - 308

- .6T = - 36

T, or amount of cheaper ($3.25 per lb) coffee to mix = highlight_green%28matrix%281%2C4%2C+%28-+36%29%2F%28-+.6%29%2C+or%2C+60%2C+lbs%29%29

You DON'T have to solve for the more expensive type, as this wasn't asked for, unless of course you don't mind doing extra work!

That's it.....nothing COMPLEX and CONFUSING!