Hello all...I have an upcoming ACT test, and I'm reviewing all of the necessary math skills. However, there is a very basic algebra practice problem, and I don't understand the solution provided in the work book. Here's the problem itself:
A grocer has two kinds of candy, one selling for $1.20 a dekagram (a tenth of a kilogram) and the other selling $1.80 a dekagram. He wants to sell a mixture of the two for $1.60 a dekagram. How much of each should he use to make 60 dekagrams of the mixture?
And here's the provided solution:
Start by assigning the value of the necessary number of dekagrams, n, of the cheaper candy at 120n cents. The number of dekagrams of the more expensive candy must be 60 – n. Therefore, the value of the more expensive candy in cents is 180(60 – n). The total value of the mixture in cents is to be 160(60).
120n + 180(60 – n) = 160(60)
I do not understand where (60 – n) comes from--? What does that represent, and how did they arrive at it? Any help would be appreciated.