At the start of the week, Crystal's bank account had a balance of $280. Each day from Monday to Friday, she used her debit card to pay $5 for parking. She wrote a check for $42 and made two deposits of $75 each. She also withdrew $200 in cash at an ATM. Which of the following expressions can be used to find the balance in Crystal's account? Select all that apply.
$280+5(5)+(-42)+2(-75)+(-200)$
$280+5(-5)+(-42)+2(75)+(-200)$
$280+5(-5)-42+2(75)-200$
$280+5(-5)-42+2(-75)-200
Answer (2)
The problem involves tracking bank transactions to find the correct expression for the final balance.
Calculate the total parking cost: 5 × ( − 5 ) = − 25 .
Account for the check: − 42 .
Calculate the total deposits: 2 × 75 = 150 .
Account for the withdrawal: − 200 .
Combine all transactions with the initial balance: 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) .
The correct expressions are: 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) and 280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 .
Explanation
Initial Analysis Let's analyze Crystal's transactions to determine the correct expression for her final bank balance. We'll start with her initial balance and then account for each transaction, noting whether it increases or decreases her balance.
Starting Balance Crystal starts with a balance of $280 . This is our starting point.
Parking Expenses From Monday to Friday, Crystal pays $5 each day for parking. Over 5 days, this totals 5 × $5 = $25 . Since this is an expense, it reduces her balance. We represent this as − 25 or 5 × ( − $5 ) .
Check Payment She writes a check for $42 , which also reduces her balance. This is represented as − 42 .
Deposits Crystal makes two deposits of $75 each, totaling 2 × $75 = $150 . These deposits increase her balance, so we represent this as + 150 or 2 × ( $75 ) .
ATM Withdrawal She withdraws $200 in cash, which reduces her balance. This is represented as − 200 .
Combining Transactions Now, let's combine all these transactions to form the expression for her final balance: 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) This simplifies to: 280 − 25 − 42 + 150 − 200
Identifying Correct Expressions Comparing our derived expression with the given options, we can identify the correct ones:
280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) - This matches our derived expression.
280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 - This is equivalent to the previous one, just written without the parentheses around the negative numbers.
Therefore, the correct expressions are: 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) $280+5(-5)-42+2(75)-200
Final Answer The expressions that correctly represent Crystal's final bank balance are:
280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) $280+5(-5)-42+2(75)-200
Examples
Understanding how to track income and expenses, like Crystal's bank account, is essential for managing personal finances. This problem demonstrates how to account for various transactions, such as daily expenses, checks, deposits, and withdrawals, to determine the final balance. This skill is crucial for budgeting, saving, and making informed financial decisions in everyday life, ensuring you always know where your money is going and how much you have available.
The correct expressions for finding Crystal's bank balance after her transactions are 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) and 280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 . These account for her parking expenses, check payment, deposits, and ATM withdrawal. Expressions that do not correctly reflect her transactions involve incorrect sign usage or calculations.
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