Question
24. Six pencils cost \( \$ 174 \). Three of the same pencils and an eraser cost \( \$ 122 \). What is the cost of the eraser? A. \( \$ 25 \) B. \( \$ 33 \) C. \( \$ 35 \) D. \( \$ 59 \)
Ask by Fowler Williams. in Jamaica
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The eraser costs \$35.
**Answer:** C. \$35
Solution
To determine the cost of the eraser, let's follow these steps:
1. **Find the cost of one pencil:**
Given that six pencils cost \$174:
\[
6p = 174 \Rightarrow p = \frac{174}{6} = 29
\]
So, one pencil costs \$29.
2. **Set up the equation for three pencils and an eraser:**
Given that three pencils and one eraser cost \$122:
\[
3p + e = 122
\]
Substitute the value of \( p \) from step 1:
\[
3(29) + e = 122 \Rightarrow 87 + e = 122
\]
3. **Solve for the cost of the eraser \( e \):**
\[
e = 122 - 87 = 35
\]
**Answer:** C. \( \$ 35 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve for the cost of the eraser, we first need to determine the cost of one pencil. If six pencils cost \( \$ 174 \), then the cost of one pencil can be calculated as follows: \[ \text{Cost of one pencil} = \frac{174}{6} = 29 \] Next, we can plug this value into the second part of the problem where three pencils and an eraser cost \( \$ 122 \): \[ 3 \times 29 + \text{Cost of eraser} = 122 \] Calculating the cost of three pencils: \[ 87 + \text{Cost of eraser} = 122 \] Now, isolating the cost of the eraser: \[ \text{Cost of eraser} = 122 - 87 = 35 \] Therefore, the cost of the eraser is \( \$ 35 \). So, the correct answer is C. \( \$ 35 \).
