Question

Eva has an account at school to purchase lunch. At the beginning of May, the account has a balance of $40. No additional

money will be added to the account for the remainder of the school year. Each school lunch costs $2.50. Let n represent the
number of lunches Eva purchases. Both expressions 40-2.50n and 2.50(16-n) represent the account balance after Eva
purchases n lunches. What does the 16 in the expression 2.50(16-n) represent?

Answer 1

The expression \(2.50(16-n)\) represents the remaining number of lunches Eva can purchase with her account balance. Here's how it works:

- Eva starts with an account balance of $40.
- Each school lunch costs $2.50.
- She purchases \(n\) lunches, so she spends \(2.50n\) dollars on those lunches.

To find out how many lunches she can still purchase with her remaining balance, subtract the amount she spent (\(2.50n\)) from her initial balance (\($40\)):

Remaining balance = Initial balance - Amount spent
Remaining balance = $40 - $2.50n

Now, to answer your question, let's equate this remaining balance to the expression \(2.50(16-n)\):

\[2.50(16-n) = $40 - $2.50n\]

So, the \(16\) in the expression \(2.50(16-n)\) represents the number of lunches (or meal equivalents) that Eva can still purchase with her remaining account balance of $40 after she has purchased \(n\) lunches.