- Represent daily withdrawals of \(\$20\) over \(5\) days as \(-20 \times 5\).
- Represent the deposit of \(\$45\) as \(+45\).
- Combine these values to get the total change: \(-20 \times 5 + 45\).
- The final expression is \(\boxed{a}\).
Explanation
- Analyzing the Financial Transactions
We need to determine the mathematical expression representing the total change in Indira's bank account. Indira made a series of withdrawals and a deposit. Withdrawals decrease the account balance, which we represent as negative values, while deposits increase the balance, which we represent as positive values.
The key data points are:
- Withdrawal amount: \(\$20\) per day.
- Duration of withdrawals: \(5\) days.
- Deposit amount: \(\$45\).
Since each withdrawal of \(\$20\) is a decrease of \(\$20\), a single withdrawal is \(-20\). Doing this for \(5\) days results in a total change of \(-20 \times 5\). The subsequent deposit of \(\$45\) is an increase, so we add \(\$45\) to the total change.
- Constructing and Selecting the Expression
To find the net change, we combine the change from the withdrawals and the change from the deposit.
The change from withdrawals is:
\[-20 \times 5\]
Adding the deposit of \(\$45\) gives us the total expression:
\[-20 \times 5 + 45\]
Comparing this result to the given options:
A\(-20 \times 5 + 45\)
B\(20 - 5 + 45\)
C\(-20 + 5 + 45\)
D\(20 \times 5 + 45\)
The expression \(-20 \times 5 + 45\) matches option a.
Examples
Understanding how to represent gains and losses algebraically is essential for managing personal finances. For instance, if you have a budget and you consistently spend a certain amount daily on coffee, you can represent your total weekly spending as a negative value. If you receive a small allowance or refund at the end of the week, you add it as a positive value. This approach helps in tracking your net savings or expenses over time, allowing for better financial planning and awareness.