Question
Kendall bought 6 notebooks and 3 pens for a total of \( \$ 27 \). The cost of one notebook is \( \$ 1.50 \) more than the cost of one pen. What is the combined cost of one notebook and one pen? Enter a numerical value in the space below. The cost of one notebook and one pen is \( \$ \)
Ask by Mcdonald Jimenez. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The combined cost of one notebook and one pen is \$5.50.
Solution
To solve the problem, let's define:
- Let \( p \) be the cost of one pen.
- Then, the cost of one notebook is \( p + \$1.50 \).
Given that Kendall bought 6 notebooks and 3 pens for a total of \$27, we can set up the equation:
\[
6(p + 1.50) + 3p = 27
\]
Simplifying the equation:
\[
6p + 9 + 3p = 27 \\
9p + 9 = 27 \\
9p = 18 \\
p = 2
\]
So, the cost of one pen is \$2, and the cost of one notebook is:
\[
2 + 1.50 = \$3.50
\]
The combined cost of one notebook and one pen is:
\[
2 + 3.50 = \$5.50
\]
**Answer:**
5.50
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Let the cost of one pen be \( x \) dollars. Then, the cost of one notebook would be \( x + 1.50 \) dollars. Now, we can set up the equation for the total cost: \[ 6(x + 1.50) + 3x = 27 \] Distributing 6 in the equation gives: \[ 6x + 9 + 3x = 27 \] Combining like terms leads to: \[ 9x + 9 = 27 \] Subtracting 9 from both sides results in: \[ 9x = 18 \] Dividing both sides by 9 gives: \[ x = 2 \] Thus, the cost of one pen is \( 2 \) dollars, and the cost of one notebook is: \[ 2 + 1.50 = 3.50 \] Now, adding the cost of one notebook and one pen: \[ 2 + 3.50 = 5.50 \] The combined cost of one notebook and one pen is \( \$ 5.50 \).
