SOLUTION: A dairy needs 244 gallons of milk containing 7% butterfat. How many gallons each each of milk containing 9% butterfat and milk containing 1% butterfat must be used to obtain the de
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Question 1165119: A dairy needs 244 gallons of milk containing 7% butterfat. How many gallons each each of milk containing 9% butterfat and milk containing 1% butterfat must be used to obtain the desired 245 gallons? Answer by greenestamps(13198) (Show Source):
A standard formal algebraic setup for solving the problem....
x = gallons of 1% butterfat
244-x = gallons of 9% butterfat
The mixture of 244 gallons is to be 7% butterfat:
That equation is solved using basic algebra, but the numbers are not "nice", so it requires a lot of work. (I leave it to you to finish solving by that method.)
Here is a quick and easy way to solve a 2-part mixture problem like this with some simple mental arithmetic.
The target percentage, 7%, is 3/4 of the way from 1% to 9%. (Picture the three percentages on a number line, if it helps....)
That means 3/4 of the total 244 gallons needs to be the 9% butterfat.
ANSWER: 1/4 of 244 gallons, or 61 gallons, of 1% butterfat milk, the other 183 gallons of 9% butterfat milk.
