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's denote the price of the first book as \( x \) and the price of the second book as \( y \).

Based on the information given, we can write the following equations:

#1: The total cost of the two textbooks is $65.
\[
x + y = 65
\]

#2: The difference in price between the two books is $9.
\[
x - y = 9
\]

Now we can solve these equations to find the values of \( x \) and \( y \).

1. From the first equation, we have:
\[
y = 65 - x
\]

2. Substitute \( y \) in the second equation:
\[
x - (65 - x) = 9
\]
\[
x - 65 + x = 9
\]
\[
2x - 65 = 9
\]
\[
2x = 74
\]
\[
x = 37
\]

3. Now substitute \( x \) back into the first equation to find \( y \):
\[
37 + y = 65
\]
\[
y = 65 - 37 = 28
\]

So, the prices of the books are:
- The cost of the first book (x) is $37.
- The cost of the second book (y) is $28.

In summary:
Let \( x = 37 \) (first book),
Let \( y = 28 \) (second book).