Question

Ellen wishes to mix candy worth $1.45 per pound with candy worth $3.74 per pound to form 27 pounds of a mixture worth $3.06 per pound. How many pounds of the more expensive candy should she use?​

Answer 1

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Answer:

  18.98 pounds

Step-by-step explanation:

Let 'e' represent the number of pounds of expensive candy Ellen should use. Then 27-e is the number of pounds of less expensive candy. Her total cost is ...

  1.45(27 -e) +3.74e = 27(3.06)

  (3.74 -1.45)e = 27(3.06 -1.45) . . . . subtract 1.45(27)

  e = 27(3.06 -1.45)/(3.74 -1.45) = 27(1.61/2.29) ≈ 18.98

Ellen should use about 18.98 pounds of the expensive candy.

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Additional comment

We showed the solution this way because it is the generic solution to any mix problem. The fraction of the mix that is the highest-value contributor is the ratio of the difference between the mix value and the lowest contributor to the difference between contributors. Here, that fraction is ...

(3.06 -1.45)/(3.74 -1.45) = (1.61/2.29)