- The initial amount is \(\$55\), and the cost of \(m\) packs of pencils at \(\$4\) each is \(4m\).
- The expression for the remaining money is \(55 - 4m\).
- Substituting \(m = 6\) into the expression gives \(55 - 4(6) = 55 - 24 = 31\).
- The final amount of money left is \(\boxed{\$31}\).
Explanation
- Defining the Expression for Remaining Money
Lily starts with \(\$55\). She buys \(m\) packs of pencils at a price of \(\$4\) per pack. The cost of one pack is \(\$4\), so the cost of \(m\) packs is \(4 \times m = 4m\) dollars. To find the remaining money, we subtract the cost of the pencils from her initial birthday money. Thus, the expression for the remaining money is \(55 - 4m\).
- Calculating the Remaining Money for m = 6
To find out how much money Lily has left after buying \(6\) packs of pencils, we substitute \(m = 6\) into our expression:
\[55 - 4m = 55 - 4(6)\]
Multiplying \(4\) by \(6\), we get \(24\). Now, subtracting this from the initial amount:
\[55 - 24 = 31\]
Therefore, after buying \(6\) packs of pencils, Lily has \(\$31\) remaining.
Examples
Understanding how to represent and calculate remaining budgets is a fundamental skill in personal finance. For instance, if you have a set amount of pocket money for the week and plan to buy snacks that cost a fixed amount each, you can use the expression \(Total - (Price \times Quantity)\) to keep track of your spending and ensure you stay within your budget. This simple algebraic modeling helps in everyday decision-making, such as planning trips, grocery shopping, or saving up for larger purchases.