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

9514 1404 393

Answer:

18.98 pounds

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.

_____

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)