Question

this question has two parts. first, answer part a. then, answer part b.
part a
incorrect
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mae wants to make more than 6 gift baskets for the school raffle. each gift basket costs $15.50. write an inequality to determine the amount of money she will spend to make the gift baskets.
part b
correct!
1 out of 1 points.

Explanation:

Step1: Define variables

Let \( n \) be the number of gift baskets and \( m \) be the amount of money spent.

Step2: Analyze the cost per basket

Each basket costs \(\$15.50\), so the total cost for \( n \) baskets is \( 15.50n \), which is equal to \( m \).

Step3: Analyze the number of baskets

Mae wants to make more than 6 baskets, so \( n > 6 \).

Step4: Relate cost and number of baskets

Since \( m = 15.50n \) and \( n > 6 \), we can substitute \( n \) in the inequality. So \( m > 15.50\times6 \), which simplifies to \( m > 93 \). But we can also write it in terms of \( n \) first. Since \( n > 6 \) and \( m = 15.50n \), the inequality for \( m \) in terms of the number of baskets is \( m>15.50n \) with \( n > 6 \), but a more direct inequality using the relationship between cost and the number of baskets (since we know the cost per basket) is: Let \( n \) be the number of baskets, \( n>6 \), and total cost \( m = 15.50n \), so the inequality for the amount of money spent is \( m > 15.50\times6\) or in terms of \( n \), \( m=15.50n \) and \( n > 6 \), so combining them, \( m>15.50\times6\) which is \( m > 93 \), but the standard way is to let \( n \) be the number of baskets, \( n>6 \), and total cost \( m = 15.50n \), so the inequality is \( m>15.50n \) where \( n > 6 \), but if we want to write it as an inequality with \( m \) and the number of baskets (since the number of baskets is more than 6), we can also write \( m>15.50\times6 \) (because if \( n > 6 \), then \( 15.50n>15.50\times6 \)). But the most appropriate inequality is \( m > 15.50n \) with \( n>6 \), but since we can express it as \( m>15.50\times6 \) (because when \( n = 6 \), cost is \( 15.50\times6 = 93 \), and since \( n>6 \), cost \( m>93 \)). However, the inequality in terms of the number of baskets and cost is \( m > 15.50n \) where \( n > 6 \), but we can also write it as \( m>15.50\times6 \) or \( m > 93 \). But the correct inequality based on the number of baskets (letting \( n \) be the number of baskets) is: Let \( n \) be the number of gift baskets, \( n>6 \), and total cost \( m = 15.50n \), so the inequality for \( m \) is \( m>15.50n \) with \( n > 6 \), but a simpler way is to note that since each basket is \( \$15.50 \) and she makes more than 6, the total cost \( m \) must be more than \( 15.50\times6 \), so \( m > 93 \). But the inequality can also be written as \( 15.50n < m \) where \( n > 6 \), but the standard form is \( m > 15.50n \) and \( n > 6 \), so combining these, we can write \( m > 15.50\times6 \) (because \( n > 6 \) implies \( 15.50n>15.50\times6 \)). So the inequality is \( m > 15.50n \) with \( n > 6 \), but if we consider \( n \) as the number of baskets (a positive integer greater than 6), then the total cost \( m = 15.50n \), so the inequality for \( m \) is \( m > 15.50\times6 \), which is \( m > 93 \). But the problem says "write an inequality to determine the amount of money she will spend to make the gift baskets", so we can let \( n \) be the number of baskets, \( n > 6 \), and \( m = 15.50n \), so the inequality is \( m > 15.50n \) where \( n > 6 \), but we can also write it as \( m > 15.50 \times 6 \) (since \( n > 6 \), the minimum number of baskets is more than 6, so the minimum cost is more than \( 15.50\times6 \)). So the inequality is \( m > 93 \) or \( m > 15.50n \) with \( n > 6 \). But the correct inequality using the number of baskets (let \( n \) be the number of baskets) is: Let \( n \) be the number of gift baskets, \( n > 6 \), and let \( m \) be the total money spent. Then \( m = 15.50n \), so substituting \( n > 6 \) into the equation for \( m \), we get \( m > 15.50\times6 \), which simplifies to \( m > 93 \). But the inequality can also be written as \( 15.50n < m \) where \( n > 6 \), but the standard way is to express the total cost in terms of the number of baskets and the inequality on the number of baskets. So the inequality is \( m > 15.50n \) with \( n > 6 \), but since we can write it as \( m > 15.50 \times 6 \) (because \( n > 6 \) implies \( 15.50n > 15.50 \times 6 \)), the inequality is \( m > 93 \) or \( m > 15.50n \) where \( n > 6 \). However, the most accurate inequality is \( m > 15.50n \) and \( n > 6 \), but we can also write it as \( m > 15.50 \times 6 \) (since \( n > 6 \), the total cost is more than \( 15.50 \times 6 \)). So the inequality is \( m > 15.50n \) with \( n > 6 \), but if we consider \( n \) as a variable representing the number of baskets (which is greater than 6), then the total cost \( m = 15.50n \), so the inequality for \( m \) is \( m > 15.50 \times 6 \), i.e., \( m > 93 \). But the problem might expect the inequality in terms of the number of baskets, so let's re - express:

Let \( n \) be the number of gift baskets. We know that \( n>6 \) and the cost \( m = 15.50n \). So the inequality for the amount of money \( m \) is \( m>15.50n \) where \( n > 6 \). But we can also write it as \( m > 15.50\times6 \) (because when \( n = 6 \), \( m = 15.50\times6=93 \), and since \( n>6 \), \( m>93 \)).

Answer:

\( m > 15.50n \) (where \( n > 6 \)) or \( m > 93 \) (a more simplified form where \( n \) is the number of baskets greater than 6 and \( m \) is the total money spent)