Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![**Problem Statement:**
Alexa has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
- She buys a new bicycle for $342.81.
- She buys 4 bicycle reflectors for $3.90 each and a pair of bike gloves for $14.51.
- She plans to spend some or all of the money she has left to buy new biking outfits for $47.72 each.
**Question:**
Which inequality can be used to determine \( o \), the maximum number of outfits Alexa can purchase while staying within her budget?
**Answer Choices:**
- ( ) \( 520 \leq 47.72 (372.92 + o) \)
- ( ) \( 520 \leq 47.72 o + 372.92 \)
- ( ) \( 520 \leq 47.72 (372.92 + o) \)
- ( ) \( 520 \leq 47.72 o + 372.92 \)
**Explanation:**
To find the correct inequality, first sum the initial expenses:
- Cost of a new bicycle: $342.81
- Cost of bicycle reflectors: \( 4 \times 3.90 = 15.60 \)
- Cost of bike gloves: $14.51
Total spent already: \( 342.81 + 15.60 + 14.51 = 372.92 \)
The remaining budget is:
\( 520 - 372.92 \)
Let \( o \) be the number of outfits she can purchase. The inequality representing her budget constraint is:
\[ 520 \geq 372.92 + 47.72o \]
Solving for \( o \) will give the maximum number of outfits Alexa can buy.
---
This problem is useful in educational settings to teach budgeting, algebraic expressions, and solving inequalities.](https://content.bartleby.com/qna-images/question/4dc66e47-5b7f-4839-a2bd-046781c4d471/0ed26835-a581-4c63-b00d-7a59f382b653/pqne3m_processed.jpeg)
Transcribed Image Text:**Problem Statement:**
Alexa has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
- She buys a new bicycle for $342.81.
- She buys 4 bicycle reflectors for $3.90 each and a pair of bike gloves for $14.51.
- She plans to spend some or all of the money she has left to buy new biking outfits for $47.72 each.
**Question:**
Which inequality can be used to determine \( o \), the maximum number of outfits Alexa can purchase while staying within her budget?
**Answer Choices:**
- ( ) \( 520 \leq 47.72 (372.92 + o) \)
- ( ) \( 520 \leq 47.72 o + 372.92 \)
- ( ) \( 520 \leq 47.72 (372.92 + o) \)
- ( ) \( 520 \leq 47.72 o + 372.92 \)
**Explanation:**
To find the correct inequality, first sum the initial expenses:
- Cost of a new bicycle: $342.81
- Cost of bicycle reflectors: \( 4 \times 3.90 = 15.60 \)
- Cost of bike gloves: $14.51
Total spent already: \( 342.81 + 15.60 + 14.51 = 372.92 \)
The remaining budget is:
\( 520 - 372.92 \)
Let \( o \) be the number of outfits she can purchase. The inequality representing her budget constraint is:
\[ 520 \geq 372.92 + 47.72o \]
Solving for \( o \) will give the maximum number of outfits Alexa can buy.
---
This problem is useful in educational settings to teach budgeting, algebraic expressions, and solving inequalities.
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