SOLUTION: Jake owns a health food store. He sells a cereal mixture that is 60 parts oatmeal, 25 parts bran, and 15 parts wheat germ. Each batch of cereal weights 80 kilograms. Jake’s problem

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Question 202652: Jake owns a health food store. He sells a cereal mixture that is 60 parts oatmeal, 25 parts bran, and 15 parts wheat germ. Each batch of cereal weights 80 kilograms. Jake’s problem is that customers are requesting more bran in the mix. They would like the batch he just prepared to have 30 parts bran out of the total 100 parts.
How many kilograms of the original mix of cereal should be removed and replaced with bran so that his customers will be satisfied?
Found 2 solutions by ankor@dixie-net.com, ptaylor:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
He sells a cereal mixture that is 60 parts oatmeal, 25 parts bran, and 15 parts wheat germ.
Each batch of cereal weights 80 kilograms.
Jake’s problem is that customers are requesting more bran in the mix.
They would like the batch he just prepared to have 30 parts bran out of the total 100 parts.
:
How many kilograms of the original mix of cereal should be removed and
replaced with bran so that his customers will be satisfied?
:
Determine what percentage is the Bran, in the original mixture
15%2F%2815%2B60%2B25%29 = 15%2F100 = .15
:
Let x = amt of mixture to be removed, and amt of bran to be added
.15(80-x) + x = .30(80)
12 - .15x + x = 24
-.15x + x = 24 - 12
.85x = 12
x = 12%2F.85
x = 14.1 kg removed, 14.1 kg of bran added

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of the original mix of cereal that should be removed and replaced with bran
Now we know that after x amount of the original mix is removed, the amount of oatmeal plus germ that remains (0.75(80-x)) does not change after the bran is added back in--just the percentage changes (0.70*80), so our equation to solve is:
0.75(80-x)=0.70*80
60-0.75x=56 subtract 60 from each side
60-60-0.75x=56-60 collect like terms
-0.75x=-4 divide each side by -0.75
x=5.333333 or 5 1/3 kilos-------------------------amount of the original mix of cereal that should be removed and replaced with bran
CK
0.75*(80-5.333333)=0.70*80
0.75(240/3 -16/3)=56
(3/4)(224/3)=56
56=56
Hope this helps---ptaylor