Question

Write two equations:
#1 Two of Julie’s textbooks are a total of $65.
#2 The difference in price between the two books is $9.

What is the cost of each book?
Let ___ = _____________
Let ___=______________

Answer 1

Let \( x \) = the cost of the first book
Let \( y \) = the cost of the second book

From the given information, we can set up the following equations:

1. **Total cost equation:**
\( x + y = 65 \)

2. **Difference in price equation:**
\( |x - y| = 9 \)

Since we generally assume \( x > y \) for simplicity, we can rewrite the second equation as:
\( x - y = 9 \)

Now we have the system of equations:

1. \( x + y = 65 \)
2. \( x - y = 9 \)

To solve these equations, we can add them:

\[
(x + y) + (x - y) = 65 + 9
\]
\[
2x = 74 \implies x = 37
\]

Substituting \( x = 37 \) back into the first equation:

\[
37 + y = 65 \implies y = 65 - 37 \implies y = 28
\]

Thus, the costs of the books are:
- The first book costs $37
- The second book costs $28

Final answer:
Let \( x = 37 \) (cost of the first book)
Let \( y = 28 \) (cost of the second book)