SOLUTION: dave wants to purchase 25 pounds of party mix for a total of $37. to obtain the mixture, he will mix nuts that cost $3 per pound with pretzels that cost $1 per pound. how many poun

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: dave wants to purchase 25 pounds of party mix for a total of $37. to obtain the mixture, he will mix nuts that cost $3 per pound with pretzels that cost $1 per pound. how many poun      Log On


   

Question 853445: dave wants to purchase 25 pounds of party mix for a total of $37. to obtain the mixture, he will mix nuts that cost $3 per pound with pretzels that cost $1 per pound. how many pounds of each type and mix should he use?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is also a mixture problem.

Account for cost and account for pounds of foods.

COST: n for nuts, p for pretzels, 1%2Ap%2B3%2An=37 or simply p%2B3n=37.

POUNDS: p%2Bn=25.

Obviously more easily viewed as a linear system problem. Two equations in the two unknowns p and n. Elimination Method here can be done mentally, at least for finding n.
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2n=12 meaning highlight%28n=6%29, therefore highlight%28p=19%29.



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More formally, coefficients on p in both equations are 1.
%28p%2B3n%29-%28p%2Bn%29=37-25
p%2B3n-p-n=12
3n-n=12
2n=12 therefore n=12%2F2=6