SOLUTION: This is the last one, I promise. How many ounces of pure bran flakes must be added to 50 oz. of cereal that is 40% bran flakes to produce a mixtue that is 50% bran flakes? Thanks

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Question 74742This question is from textbook Introductory Algebra
: This is the last one, I promise.
How many ounces of pure bran flakes must be added to 50 oz. of cereal that is 40% bran flakes to produce a mixtue that is 50% bran flakes?
Thanks so much for your help. I can now maybe do something else.
Jane This question is from textbook Introductory Algebra

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=the amount of pure bran flakes that must be added
Now we know that the amount of pure bran flakes that exists before things are mixed together must equal the amount of pure bran flakes that exists after everything is mixed together. So our equation to solve is:
x+0.40(50)=0.50(50+x) get rid of parens
x+20=25+0.50x subtract 0.50x and also 20 from both sides
x+20-20-0.50x=25-20+0.50x-0.50x collect like terms
0.50x=5 divide both sides by 0.50

x=10 oz of pure bran flakes must be added
CK
10+0.40(50)=0.50(50+10)
10+20=30
30=30
Let's try something, Jane. Obviously this cereal has both bran flakes and "otherstuff" in it. Lets work the problem by focusing on the "otherstuff" instead of the bran flakes.
We will still let x=the amount of pure bran flakes that must be added
Now we know that the amount of "otherstuff" in the pure bran flakes that are added (0) plus the amount of "otherstuff" in the 50 oz mixture 0.60(50){40% bran flakes then it must be 60% "otherstuff"} must equal the amount of "otherstuff" in the final mixture 0.50(50+x){equal amounts of "otherstuff" and bran flakes}. So our equation to solve is:
0.60(50)=0.50(50+x) get rid of parens
30=25+0.50x subtract 25 from both sides
30-25=25-25+0.50x collect like terms
5=0.50x divide both sides by 0.50
x=10 oz -----same as before

Hope this helps---ptaylor