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

To solve the problem, let's define two variables:

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

Now we can set up the equations based on the information provided:

1. The total cost of the two textbooks:
\[
x + y = 65 \quad \text{(Equation 1)}
\]

2. The difference in price between the two books:
\[
x - y = 9 \quad \text{(Equation 2)}
\]

Now we can solve the system of equations.

### Step 1: Solve Equation 2 for \( x \)
From Equation 2:
\[
x = y + 9
\]

### Step 2: Substitute \( x \) in Equation 1
Substituting \( x \) in Equation 1:
\[
(y + 9) + y = 65
\]

Combine the \( y \) terms:
\[
2y + 9 = 65
\]

### Step 3: Solve for \( y \)
Subtract 9 from both sides:
\[
2y = 56
\]
Divide by 2:
\[
y = 28
\]

### Step 4: Find \( x \)
Now substitute \( y \) back into the equation for \( x \):
\[
x = y + 9 = 28 + 9 = 37
\]

### Conclusion
The costs of the textbooks are:
- The first textbook cost \( x = 37 \).
- The second textbook cost \( y = 28 \).

Thus, the final answer is:
- Let \( x = 37 \)
- Let \( y = 28 \)