Question
Create the system of linear inequalities that models the following situation. The field hockey team at school is hosting a fundraiser. They hope to raise at least $600. They are selling chocolate for $4 and flowers for $5. The team captain estimates they will sell no more than 150 items, but they know that 50 flowers have already been preordered.(1 point) Responses 4x+5y≥600, x+y≥150, y≤50 4 x plus 5 y greater-than-or-equal-to 600 , x plus y greater-than-or-equal-to 150 , y less-than-or-equal-to 50 4x+5y≥600, x+y≤150, y≥50 4 x plus 5 y greater-than-or-equal-to 600 , x plus y less-than-or-equal-to 150 , y greater-than-or-equal-to 50 4x+5y>600, x+y≥150, y≥50 4 x plus 5 y greater than 600 , x plus y greater-than-or-equal-to 150 , y greater-than-or-equal-to 50 4x+5y≥600, x+y≥150, y≥50
Answers
GPT-4o mini
To model the situation with a system of linear inequalities, we can define variables for the number of items sold:
- Let \( x \) be the number of chocolate items sold.
- Let \( y \) be the number of flower items sold.
Now let's formulate the inequalities based on the problem:
1. **Total revenue from selling chocolates and flowers:**
The team wants to raise at least $600. The revenue from selling chocolates is \( 4x \) (since each chocolate costs $4) and from flowers is \( 5y \) (since each flower costs $5). Therefore, the inequality for the amount they want to raise can be expressed as:
\[
4x + 5y \geq 600
\]
2. **Total items sold:**
The team captain estimates they will sell no more than 150 items in total. This can be represented as:
\[
x + y \leq 150
\]
3. **Preordered flowers:**
They know that 50 flowers have already been preordered, so they must sell at least those 50 flowers. This is given by:
\[
y \geq 50
\]
Putting it all together, the complete system of inequalities is:
1. \( 4x + 5y \geq 600 \)
2. \( x + y \leq 150 \)
3. \( y \geq 50 \)
Therefore, among the provided options, the correct inequalities that model the situation are:
\[
4x + 5y \geq 600, \quad x + y \leq 150, \quad y \geq 50
\]
- Let \( x \) be the number of chocolate items sold.
- Let \( y \) be the number of flower items sold.
Now let's formulate the inequalities based on the problem:
1. **Total revenue from selling chocolates and flowers:**
The team wants to raise at least $600. The revenue from selling chocolates is \( 4x \) (since each chocolate costs $4) and from flowers is \( 5y \) (since each flower costs $5). Therefore, the inequality for the amount they want to raise can be expressed as:
\[
4x + 5y \geq 600
\]
2. **Total items sold:**
The team captain estimates they will sell no more than 150 items in total. This can be represented as:
\[
x + y \leq 150
\]
3. **Preordered flowers:**
They know that 50 flowers have already been preordered, so they must sell at least those 50 flowers. This is given by:
\[
y \geq 50
\]
Putting it all together, the complete system of inequalities is:
1. \( 4x + 5y \geq 600 \)
2. \( x + y \leq 150 \)
3. \( y \geq 50 \)
Therefore, among the provided options, the correct inequalities that model the situation are:
\[
4x + 5y \geq 600, \quad x + y \leq 150, \quad y \geq 50
\]