SOLUTION: Chocolate costing $10 per pound is mixed with nuts costing $4 per pound to make a mixture costing $6 per pound. What fraction of the mixture's weight is chocolate? Express your ans
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Question 1117739: Chocolate costing $10 per pound is mixed with nuts costing $4 per pound to make a mixture costing $6 per pound. What fraction of the mixture's weight is chocolate? Express your answer as a common fraction.
Asking for the fraction of the weight of the mixture that is chocolate makes it easy to solve the problem without algebra.
The cost per pound of the mixture ($6) is 1/3 of the way from the cost per pound of the nuts ($4) to the cost per pound of the chocolate ($10); that means 1/3 of the mixture is chocolate.
Because no weights are given in the statement of the problem, a solution using algebra is a bit awkward....
Let the mixture be x pounds of chocolate and y pounds of nuts; then the number we are looking for is the weight of the chocolate divided by the total weight: x/(x+y).
The x pounds of chocolate at $10 per pound and the y pounds of nuts at $4 per pound make (x+y) pounds of a mixture at $6 per pound:
And the fraction of the mixture that is chocolate is
