A. At the beginning of the month, Evan had $24 in his account at the school bookstore. 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? i. First he bought some notebooks and pens that cost $16.
ii. Then he deposited some more money and his account balance was $28.
iii. Then he bought a book for English class that cost $34.
iv. Then he deposited exactly enough money so that he paid off his debt to the bookstore.
b. Explain why it makes sense to use a negative number to represent Evan's account balance when he owes money.
IM Commentary
Many people like to use debt to help students understand negative numbers. When doing so, it is important to keep in mind that representing debt with negative numbers is a convention, and that it would be possible to talk about debt without ever using negative numbers. For example, if I borrow $30 from my cousin, I owe her +30 dollars. If I give her $40, then she owes me +10 dollars. The reason it is so convenient to represent debt with negative numbers is that it allows us to use arithmetic and algebra to keep track of who owes what to whom. Despite the fact that it is convenient to do
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