Question
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Anna has \( \$ 65 \) to spend on dress, shoes and accessories for a party. If the cost of the dress and shoes is more than \( \$ 50 \), which inequality represents the dollar amount, \( p \) Anna can spend on accessories? A) \( p>115 \) C) \( p>15 \) B) \( p<115 \) D) \( p<15 \) Untitled Question * 1 point A) \( p>115 \) B) \( p<115 \) C) \( p>15 \) D) \( p<15 \)

Ask by Stanley Vargas. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

The inequality representing the amount Anna can spend on accessories is \( p < 15 \).

Solution

To determine the inequality that represents the amount \( p \) Anna can spend on accessories, let's break down the information: 1. **Total Budget:** Anna has \( \$65 \) to spend on dress, shoes, and accessories. 2. **Cost of Dress and Shoes:** The combined cost of the dress and shoes is more than \( \$50 \). Let: - \( d \) = cost of the dress - \( s \) = cost of the shoes - \( p \) = cost of the accessories We can set up the following inequalities based on the given information: 1. \( d + s > 50 \) (The combined cost of dress and shoes is more than \( \$50 \)) 2. \( d + s + p \leq 65 \) (Total spending must not exceed \( \$65 \)) From the first inequality, we know that \( d + s > 50 \). Substituting this into the second inequality: \[ p \leq 65 - (d + s) < 65 - 50 = 15 \] Thus, the maximum Anna can spend on accessories is less than \( \$15 \). **Answer:** D) \( p < 15 \)

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Extra Insights

To solve this problem, we start with the total amount Anna has, which is \( \$ 65 \). Since the cost of the dress and shoes is more than \( \$ 50 \), we can express this as \( d + s > 50 \), where \( d \) is the cost of the dress, and \( s \) is the cost of the shoes. Now, the amount she can spend on accessories \( p \) can be found by subtracting the cost of the dress and shoes from her total amount: \[ p = 65 - (d + s) \] Since \( d + s > 50 \), we can write: \[ p < 65 - 50 \] \[ p < 15 \] Thus, the correct inequality representing the dollar amount Anna can spend on accessories is \( p < 15 \). The answer is D) \( p < 15 \). So, only \( \$ 15 \) or less can go towards accessories if she spends over \( \$ 50 \) on the dress and shoes!

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