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 correct expressions for Crystal's bank account balance after her transactions are 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) and 280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 . Both correctly account for the expenses and deposits she made. The incorrect expressions either add expenses or mistakenly subtract deposits instead of adding them.
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The initial balance is $280.
Calculate total expenses: Parking costs $5 \times 5 = $25, check for $42, and ATM withdrawal of $200.
Calculate total deposits: Two deposits of $75 each, totaling $2 \times 75 = $150.
The correct expressions are: 280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) and 280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 .
Explanation
Analyzing the Problem We need to determine which of the given expressions correctly calculates Crystal's final bank account balance after several transactions. Let's analyze each transaction and how it affects the initial balance.
Calculating Parking Costs Crystal starts with a balance of $280. She incurs daily parking fees of $5 from Monday to Friday, totaling 5 days. This means a total expense of $5 \times 5 = $25 for parking. This will reduce her balance.
Accounting for the Check She writes a check for $42, which also reduces her balance.
Calculating Deposits She makes two deposits of $75 each, totaling $2 \times 75 = $150. These deposits increase her balance.
Accounting for the Withdrawal She withdraws $200 from an ATM, which reduces her balance.
Formulating the Expression Now, let's combine all these transactions to create an expression for her final balance: 280 − 5 ( 5 ) − 42 + 2 ( 75 ) − 200 This expression represents the initial balance, minus the total parking cost, minus the check amount, plus the total deposits, and minus the ATM withdrawal.
Comparing with Given Options Let's compare this expression with the given options:
280 + 5 ( 5 ) + ( − 42 ) + 2 ( − 75 ) + ( − 200 ) : This is incorrect because it adds the parking cost instead of subtracting it, and it subtracts the deposits instead of adding them.
280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 ) : This is correct because it subtracts the parking cost, subtracts the check amount, adds the deposits, and subtracts the withdrawal.
280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200 : This is also correct and is equivalent to the previous correct option.
280 + 5 ( − 5 ) − 42 + 2 ( − 75 ) − 200 : This is incorrect because it subtracts the deposits instead of adding them.
Identifying Correct Expressions Therefore, the correct expressions are:
280 + 5 ( − 5 ) + ( − 42 ) + 2 ( 75 ) + ( − 200 )
280 + 5 ( − 5 ) − 42 + 2 ( 75 ) − 200
Examples
Understanding bank account transactions is crucial in personal finance. For example, if you start with a balance of $500, spend $20 daily for 7 days on lunch, receive two deposits of $100 each, and pay a bill of $150, you can calculate your final balance using a similar expression: 500 − 7 ( 20 ) + 2 ( 100 ) − 150 . This helps you track your spending, manage your budget, and avoid overdraft fees.
