Write two equations:

Question

#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 \( y = 28 \)