Question
Miriam withdraws $19 from her bank account once each day for six days. What integer represents the change in the amount in the account? Use pencil and paper. Find the integer that would represent the change in the amount in the account if Miriam deposits $19 into her bank account once each day for six days. Explain the difference between the integer for the withdrawals and the integer for the deposits.
Answers
GPT-4o mini
To find the change in Miriam's bank account due to her actions, we can represent withdrawals and deposits using integers:
1. **Withdrawals:**
- Miriam withdraws $19 each day for 6 days.
- The total amount withdrawn = $19 × 6 = $114.
- Since a withdrawal decreases the balance in the account, we represent this with a negative integer.
- Therefore, the change in her account due to withdrawals is -114.
2. **Deposits:**
- Now, if Miriam deposits $19 each day for 6 days, the total amount deposited is also $19 × 6 = $114.
- Since a deposit increases the balance in the account, we represent this with a positive integer.
- Therefore, the change in her account due to deposits is +114.
### Summary:
- **Change due to withdrawals:** -114
- **Change due to deposits:** +114
### Explanation of the difference:
The difference between the integer for the withdrawals (-114) and the integer for the deposits (+114) lies in their signs:
- Withdrawals result in a negative change because the money is being taken out of the account.
- Deposits result in a positive change because money is being added to the account.
In mathematical terms, the withdrawals represent a decrease in funds, while deposits represent an increase in funds. This is why their values are equal in magnitude (both $114), but opposite in sign.
1. **Withdrawals:**
- Miriam withdraws $19 each day for 6 days.
- The total amount withdrawn = $19 × 6 = $114.
- Since a withdrawal decreases the balance in the account, we represent this with a negative integer.
- Therefore, the change in her account due to withdrawals is -114.
2. **Deposits:**
- Now, if Miriam deposits $19 each day for 6 days, the total amount deposited is also $19 × 6 = $114.
- Since a deposit increases the balance in the account, we represent this with a positive integer.
- Therefore, the change in her account due to deposits is +114.
### Summary:
- **Change due to withdrawals:** -114
- **Change due to deposits:** +114
### Explanation of the difference:
The difference between the integer for the withdrawals (-114) and the integer for the deposits (+114) lies in their signs:
- Withdrawals result in a negative change because the money is being taken out of the account.
- Deposits result in a positive change because money is being added to the account.
In mathematical terms, the withdrawals represent a decrease in funds, while deposits represent an increase in funds. This is why their values are equal in magnitude (both $114), but opposite in sign.