Question

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.

Answer 1

Evan's transactions at the school bookstore can be represented by algebraic equations using a variable x. In each transaction, he added or subtracted amounts from his starting balance of $24, managed to pay off a debt, and ended up with zero debt.

Step-by-step explanation:

Let's represent the unknown quantity of money Evan spent or deposited with the variable x.

1. First, he bought some notebooks and pens that cost $16. If he had $24 initially, the new balance is represented by the equation 24 - 16 = x, which gives us x = $8. This represents his new balance.
2. Then he deposited some more money and his account balance was $28. To find out the amount he deposited, we use the equation 8 + x = 28, leading to x = $20, the amount he deposited.
3. Next, he bought a book for his English class that cost $34. Now the transaction can be represented as 28 - 34 = x, which gives us x = -$6. This means he has a debt of $6.
4. Lastly, he deposited exactly enough money so that he paid off his debt to the bookstore. This transaction is represented as -6 + x = 0, which means x = $6, the amount he deposited to clear the debt.

To represent these transactions on a number line, you would start at $24, move left (subtract) when he spends money, and move right (add) when he deposits money.