Cindy wrote two checks for \$200 and \$350, and then deposited cash into her account. If her account balance increased by \$150 after these transactions, which of the following could be the amount of the third check and the cash that Cindy deposited?

• A. Third check: \$400; Cash deposited: \$700
• B. Third check: \$100; Cash deposited: \$800
• C. Third check: \$250; Cash deposited: \$500
• D. Third check: \$300; Cash deposited: \$600

Answer: (B)

Verified step by step guidance

1. Step 1: Begin by understanding the problem. Cindy's account balance increased by \$150 after writing two checks and depositing cash. The goal is to determine the correct combination of the third check amount and the cash deposited.
2. Step 2: Write down the equation for the account balance change. The account balance change is calculated as: \( \text{Cash Deposited} - (\text{Check 1} + \text{Check 2} + \text{Third Check}) \). Substitute the values for Check 1 (\$200) and Check 2 (\$350).
3. Step 3: Rearrange the equation to solve for the relationship between the third check and the cash deposited. The equation becomes: \( \text{Cash Deposited} - \text{Third Check} = \text{Account Balance Increase} + (\text{Check 1} + \text{Check 2}) \). Substitute the known values: \( \text{Cash Deposited} - \text{Third Check} = 150 + (200 + 350) \).
4. Step 4: Simplify the equation to find the total amount of cash deposited minus the third check. This gives: \( \text{Cash Deposited} - \text{Third Check} = 700 \).
5. Step 5: Test each option provided in the problem to see which combination of the third check and cash deposited satisfies the equation \( \text{Cash Deposited} - \text{Third Check} = 700 \). For example, substitute \( \text{Third Check} = 100 \) and \( \text{Cash Deposited} = 800 \) into the equation to verify if it holds true.