Question

A vending machine sells chips at $0.40 and candy at $0.50. Last month, the vending machine yielded $139.80 with a sale of 298 items. how many packages of chips were purchased last month

Answer 1

Let us say... . the machine sold packages of chips at the amount of "p",
and the machine also sold, last month as well, an amount of "c" candies

now, last month the machine sold total 298 items
that yielded a revenue of $139.80

so...whatever "p" and "c" are, we know that, their sum for last month is,
298, so,
p + c = 298

how much revenue in sales of chips? well, they're 0.40 per package,
so, whatever "p" is, the machine sold 0.40 * p or 0.4p in revenue

how much for the candies? well, they're 0.50 for each, so
whatever "c" is, 0.50 * c or 0.5c in revenue

we know, their total revenue yield was 139.80
so
0.4p + 0.5c = 139.8

now... do substitution from the 1st equation on the 2nd one, and solve for "p", or packages of chips

that is $\begin{cases} p+c=298\to c=\boxed{298-p} \\ \quad \\ 0.4p+0.5c=139.8 \\ \textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\ 0.4p+0.5(\boxed{298-p})=139.8 \end{cases}\impliedby \textit{solve for "p"}$