SOLUTION: Marcus is inventing a new cookie recipe. He'd like the recipe to contain both walnuts and gourmet chocolate chip chunks. Walnuts sell for $2.40 per pound and gourmet chips sell for

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Question 184883: Marcus is inventing a new cookie recipe. He'd like the recipe to contain both walnuts and gourmet chocolate chip chunks. Walnuts sell for $2.40 per pound and gourmet chips sell for $3.00 per pound. How many pounds of walnuts should be mixed with 3 pounds of gourmet chips to obtain a mixture selling for $2.58 per pound?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = pounds of walnuts needed
Let m = pounds of the final mixture
In words:
(pounds of walnuts)x(price per pound) + (pounds of chips)x(price per pound)
=(pounds of mixture)x(price per pound)
given:
Price of walnuts in mixture = 2.4w
Price of chips in mixture = 3%2A3+=+9
Price of mixture = 2.58m
m+=+3+%2B+w
--------------
2.4w+%2B+9+=+2.58m
2.4w+%2B+9+=+2.58%2A%283+%2B+w%29
2.4w+%2B+9+=+7.74+%2B+2.58w
.18w+=+1.26
w+=+7
7 pounds of walnuts are needed
check:
2.4w+%2B+9+=+2.58m
2.4%2A7+%2B+9+=+2.58m
16.8+%2B+9+=+2.58m
2.58m+=+25.8
m+=+10
and
m+=+3+%2B+w
10+=+3+%2B+7
10+=+10
OK