Lesson 4: Money and Debts

Let's apply what we know about signed numbers to money.

4.1: Concert Tickets

Priya wants to buy three tickets for a concert. She has earned \$135 and each ticket costs \$50. She borrows the rest of the money she needs from a bank and buys the tickets.

  1. How can you represent the amount of money that Priya has after buying the tickets?
  2. How much more money will Priya need to earn to pay back the money she borrowed from the bank?
  3. How much money will she have after she pays back the money she borrowed from the bank?

4.2: Cafeteria Food Debt

At the beginning of the month Kiran had \$24 in his school cafeteria account. Use a variable to represent the unknown quantity in each transaction below and write an equation to represent it. Then, represent each transaction on a number line. What is the unknown quantity in each case?

  1. In the first week he spent \$16 on lunches. How much was in his account then?
  2. Then he deposited some more money and his account balance was \$28. How much did he deposit?
  3. Then he spent \$34 on lunches the next week. How much was in his account then?
  4. Then he deposited enough money to pay off his debt to the cafeteria. How much did he deposit?
  5. Explain why it makes sense to use a negative number to represent Kiran's account balance when he owes money.

4.3: Bank Statement

Here is a bank statement.

A checking account statement for Andre person. A 5-column table shows the activity in his account for the month of October. Column 1 is labeled “Date,” column 2 is labeled “Description,” column 3 is labeled “Withdrawals,” column 4 is labeled “Deposits,” and column 5 is labeled “Balance.” There are 8 rows describing each transaction Andre made with the bank. Row 1: Date: 10, 3, 2017; Description, Previous balance; Withdrawals, blank; Deposits, blank; Balance, 39 point 8 7 dollars. Row 2: Date: 10, 5, 2017; Description, Check Number 256; Withdrawal, 28 point 5 0 dollars; Deposits, blank; Balance, 11 point 37 dollars. Row 3: Date: 10, 6, 2017; Description, A T M deposit – Cash; Withdrawals, blank; Deposit, 45 point 0 0 dollars; Balance, 56 point 3 7 dollars. Row 4: Date: 10, 10, 2017; Description, Wire transfer; Withdrawals, 37 point 9 1 dollars; Deposits, blank; Balance: 18 point 4 6 dollars. Row 5: Date: 10, 17, 2017; Description, Point of Sale Grocert Store; Withdrawals, 16 point 4 3 dollars. Deposits, blank; Balance, 2 point 0 3 dollars. Row 6: Date: 10, 25, 2017; Description, Funds Transfer from Savings; Withdrawals, blank; Deposits, 50 point 0 0 dollars; Balance, 52 point 0 3 dollars. Row 7: Date: 10, 28, 2017; Description, Check Number 257; Withdrawals, 42 point 0 0 dollars; Deposits, blank; Balance, 10 point 0 3 dollars. Row 8: Date 10, 29, 2017; Description, Online Payment Phone Services; Withdrawals, 72 point 5 0 dollars; Deposits, blank; Balance, negative 62 point 4 7 dollars. Money Bag Copyright Owner: security_man License: Public Domain Via: openclipart.org

  1. If we put withdrawals and deposits in the same column, how can they be represented?

  2. Andre withdraws \$40 to buy a music player. What is his new balance?

  3. If Andre deposits \$100 in this account, will he still be in debt? How do you know?

Summary

Banks use positive numbers to represent money that gets put into an account and negative numbers to represent money that gets taken out of an account. When you put money into an account, it is called a deposit. When you take money out of an account, it is called a withdrawal.

People also use negative numbers to represent debt. If you take out more money from your account than you put in, then you owe the bank money, and your account balance will be a negative number to represent that debt. For example, if you have \$200 in your bank account, and then you write a check for \$300, you will owe the bank \$100 and your account balance will be -\$100.

  starting balance deposits and withdrawals new balance
row 1 0 50 $0 + 50$
row 2 50 150 $50 + 150$
row 3 200 -300 $200 + (\text-300)$
row 4 -100    

In general, you can find a new account balance by adding the value of the deposit or withdrawal to it. You can also tell quickly how much money is needed to repay a debt using the fact that to get to zero from a negative value you need to add its opposite.

Practice Problems ▶

Glossary

withdrawal

withdrawal

When you take money out of a bank account, it is called making a withdrawal from the account, or withdrawing money from the account.

deposit

deposit

When you put money into a bank account, it is called making a deposit into the account, or depositing money in the account.